What observations would be needed to falsify the law of conservation of energy? I've been doing some thinking, and began to wonder: What observations have led us to the conclusion that ‘energy can neither be created nor destroyed’?
Essentially, this means that the big bang supplied our universe with all the matter that currently exist in it.
My question is, if this were untrue for some reason (despite what math tells us) - and there were more ‘atoms’, ‘quarks’ or ‘bits’ being added to the system, how would we tell? What would that look like?
What experiment would be used to detect ‘more matter’ existing now than during the big bang?
Is this simply a matter of creating instruments that measure more accurately, or would some clever experiment need to be devised?
I've read several answers on this and other sites that explain the law of conservation of energy, but none that nail the hypothetical question above.
 A: 
What observations would be needed to falsify the law of conservation of energy?

As far as I understand there is no set of observations imaginable from which to draw such a conclusion. The only related conclusion, or measurement, which could be drawn from a suitable set of experimental observations would be: that a particular experimental region (containing the participants whose observations were collected and analyzed) had not been "closed"; which may or may not agree with expectations and/or results of preceding trials.
Asking for the possibility of falsifying "the law of conservation of energy" is about as pointless as asking for the possibility of "falsifying" what we mean by the statements "this system was closed" or "this system was not closed".

if [...] there were more ‘atoms’, ‘quarks’ or ‘bits’ being added to the system, how would we tell?  

Well, supposedly it is possible to count "atoms", and "quarks", at least, in any particular finite region of interest. (I wrote "supposedly", because I'm not quite certain how the possibility of baryon number violation, even in the Standard Model, for instance, may impair such attempts.)

What experiment would be used to detect ‘more matter’ existing now than during the big bang?

"Existing now" in which region?,
"during the big bang" in which region? ...
A: Conservation of Energy can be derived if one accepts that $F = ma$. I won't include the derivation here unless you ask. This means that to prove Conservation of Energy wrong, one must prove $F = ma$ wrong. This could be attempted in a variety of ways. One such way would be applying a force to an object and noticing the $F = ma$ doesn't give the correct acceleration.
