Could dark matter be curved pockets of spacetime left over from the big bang? My understanding of general relativity is that gravitation is equivalent to spacetime curvature and is proportional relative to localized mass. Traditionally, we conceptualize that massive things attract each other by bending spacetime. Could some mechanism in the early Universe have warped spacetime and thereafter massive objects attracted to, or "fell into," these areas of warping thus giving us the difference between calculated galactic masses and observed activity?
In other words, at this scale, rather than mass bending spacetime, perhaps warps in spacetime have collected mass. Has this been ruled out as the source of dark matter?
Clarification edit:
Thanks for the great explanations! Much of this I knew, it's the maths I'm not so familiar with. My initial question wasn't clear enough.
Of course warped spacetime would affect normal matter as well, which is why we see galaxies in those places. I wasn't meaning that DM, normal matter, and this warping exists, but that the warping is what we call DM.
Suppose that "first" there were some statistical outlying warpings of ST geometry, which collect normal matter, which further the warping, which collect more normal matter, etc. as a feedback loop. Thus DM would be the difference between the warping from normal matter and normal flat spacetime curvature, as opposed to some exotic form of matter that is warping spacetime.
 A: A footnote to Bob's answer.
It has been suggested that warped spacetime could behave like a mass without any matter being present. An example of this is the geon suggested by John Wheeler. So in the context of your idea the suggestion would be that in the very early stages of the universe the extreme conditions might have formed geons and these could be responsible for the unknown extra matter.
It's a tempting idea, but probably doesn't work. We don't know whether geons can be stable. There have been various attempts to construct them but with no definitive results. And even if geons were stable there's no obvious mechanism for them to have been formed in the Big Bang and subsequent evolution of the universe. So it doesn't seem they are likely to be responsible for the dark matter.
A: I'll answer, and don't think it's a bad question. We don't know what dark matter (DM) is but do know a few things about DM that make your proposed cause of it not likely, or not relevant. But you do bring up some possibilities in the early universe, although not exactly like what is thought possible. I explain below. 
In any event I encourage to keep asking, and answering, the downvotes and rules are easy to get used to and understand a bit how to deal with.  encourage you to read more on cosmology and gravitation, if it interests you. 
The main reason your proposed mechanism for DM is not possible or relevant is that is does not explain how DM is different than regular matter. Your explanation holds equally if it was normal matter. First, your proposed early universe high curvature that could have attracted DM, also would have attracted normal matter. It would be no different. And it would have continued to do so and set the nucleus for stars and galaxies. Secondly, as @Mladen said in the comment, dark matter does not interact significantly with regular matter or with itself (it does interact gravitationally which is how we detect it), while regular matter does. This is known because we have astronomical evidence of two galaxies passing through each other with the regular matter slowed down by collisions/interactions, and DM not that much affected (with the dark matter density estimated by the gravitational effects). See the bullet cluster for this at   https://en.m.wikipedia.org/wiki/Bullet_Cluster. 
So, even if you are right, your explanation would be right for both DM and normal matter. Nothing that explains dark matter.  
Now, as for the possibility of high curvature early in the universe, with some areas much higher than other, you have to be careful as to when. We know that after 380000 years the cosmic microwave background (CMB) was let loose (after decoupling), and it is extremely homogeneous and isotropic. We don't see anything that looks like there were were disparate areas, with some really high curvature someplace. So, it must have been way before or way after. After recombination we know and see a lot about the universe evolution, and there's no evidence nor reason for it. Even before we don't see much reasons. See the standard possible thoughts on what DM could be at https://en.m.wikipedia.org/wiki/Dark_matter
The very early universe, before inflation, could possibly have formed very large strings and string walls (from string theory), and have caused topological defects. This could be some of what was around during the Planck time and some may have been leftover as relics, according to string theory, if string theory is true in some way (which remains TBD, with less optimism for it that there used to be). But at those early times if there were string or string walls, gravitation would still not have been what we envision now, curvature, it would have been more stringy things interacting, in ways we don't know.  Most thoughts of the DM is that it represents some relic particles formed in the early universe. If formed then, doesn't matter if they would have been attracted by a high curvature. 
But we've not been able to identify any dark matter particles, and it is still a research area.  
See a summary PDF on some possible early universe relics at https://arxiv.org/abs/1202.5851. There are other related articles, but nothing definitive.
CLARIFICATION EDIT RESPONSES
The clarification to the question is whether some 'strange and strong' warping of spacetime might be what creates the effects we call DM. So she is not asking whether the warping can create exotic new particles that are then the DM, but where it is the DM. 
There's some reasons why that's not likely, but first let me say something about would need to be involved to create something like that, in my view. There would have to be vacuum macroscopic solutions of GR where is is some stable region with a gravitational field similar to that created by some distribution of matter locally (since that is what it looks to us, e.g., in the halo of galaxies). The geons that Wheeler proposed seem to not be stable, but not proven. The other possibility involves some other semi-stable, exact solution of GR in vacuum where the gravitational field looks like it's caused in a local region. There are GR vacuum solution with a semi-stable or stable region of high gravity. An example are solitons, which can be in the form of soliton waves or other configurations, and with possible configurations like kinks and walls. Those have been explored and it is hard to find those kinds of solutions. Since GR is nonlinear you can't add one solution to the other one, the effects that cause the solitons are nonlinear. They do not exist in the linear approximations. It is thought that some of those could have been relics from the early universe, as in my reference above. There could be other solutions that allow it that have not been found. See the classic treatment for gravitational solitons at https://www.abebooks.co.uk/Gravitational-Solitons-V-BELINSKI-E-VERDAGUER/18734763538/bd.  It's a book by those two authors, and not cheap, and you can't read it online for free. There's been more papers over the years, and you can google gravitational solitons. And there could some other solutions that fit better the DMs we see.
WHY UNLIKELY 
First, they would have had to have been created early in the universe with initially a pretty homogeneous and isotropic distributions in the large. Then thaose would have had to have the property that they not be that cohesive, i.e., that a very large number of much smaller lumps can happen, it, they'd have to be splittable into mass particle-like things, or smaller than galaxy lumps of those. That seems highly unlikely unless they were particle or so sized, i.e., each one was a DM particle. And now we're back where we started. 
Postulating any other form would require backing via calculations of some of those soliton solutions and how they might break up into smaller ones. I have not seen any. It's just not easy in GR to find general solutions.
So if you wish to try to postulate that, there's a lot of calculations to be done to show plausibility.
