You can look at databases of binary stars to tell you what the range of orbital periods/separations of stars currently are. Unfortunately that isn't going to answer your question because many short-period binary systems have evolved to be that way - e.g. the short-period cataclysmic variable stars or the "contact" binaries known as W UMa systems, where the stars are actually touching each other and have a common envelope. Binaries can also be made "harder" by interactions with third bodies, especially during their early lives if they are born in dense star clusters. Hence there are many short period binary systems with periods shorter than one day, where the components are barely separated, or are not separated at all.

What you need to do is look for a catalogue of binary objects in the youngest star forming regions or star clusters, where you might reasonably assume there has been little time for interaction (to some extent it depends whether you include early life in a star forming environment as part of the birth process or not).

It is actually quite hard to do surveys of this kind. You need repeated, high resolution spectroscopic measurements of quite faint objects in order to find the doppler shifts due to binary motion. But some work is out there. Meibom et al. (2006) search for spectroscopic binaries in the young(ish) clusters M34 and M35 (250 and 150 Ma respectively). They find 6 binaries in these clusters which have separations smaller than 0.12 au and periods below 13 days. The shortest period binary has a $0.9M_{\odot}$ primary with a period of 2.25 days. Nevertheless, the authors concede that these binaries may have been hardened by close third-body encounters.

Morales-Calderon et al. (2012) pursued a different approach; performing photometric monitoring in the infrared to search for eclipsing binaries in the very young Orion Nebula cluster (age about 2 Ma). They found six binaries with periods between 3.9 and 20.5 days.

There are then quite a few other individual results and studies. I can't immediately locate any good compilation, but this is the closest binary that a brief search uncovered: Bakis et al. (2011) analysed the binary IM Mon, probably a 10 Ma old system in Orion. They find an orbital period of only 1.19 days and primary and secondary masses of 5.5 and 3.3$M_{\odot}$. Their radii are about 30% of the separation between the stellar centres (estimated to be $a=9.77R_{\odot} = 0.045$ au). The comparative youth and mass of this binary suggest it was probably "born this way".

You can look at databases of binary stars to tell you what the range of orbital periods/separations of stars currently are. Unfortunately that isn't going to answer your question because many short-period binary systems have evolved to be that way - e.g. the short-period cataclysmic variable stars or the "contact" binaries known as W UMa systems, where the stars are actually touching each other and have a common envelope. Binaries can also be made "harder" by interactions with third bodies, especially during their early lives if they are born in dense star clusters, or the orbits may be shrunk or the stars may even merge due to gas-induced orbital decay during the early embedded phase of the formation of a star cluster (Korntreff et al. 2012) . Hence there are many older short period binary systems with periods shorter than one day, where the components are barely separated, or are not separated at all.

What you need to do is look for a catalogue of binary objects in the youngest star forming regions or star clusters, where you might reasonably assume there has been little time for interaction (to some extent it depends whether you include early life in a star forming environment as part of the birth process or not).

It is actually quite hard to do surveys of this kind. You need repeated, high resolution spectroscopic measurements of quite faint objects in order to find the doppler shifts due to binary motion. But some work is out there. Meibom et al. (2006) search for spectroscopic binaries in the young(ish) clusters M34 and M35 (250 and 150 Ma respectively). They find 6 binaries in these clusters which have separations smaller than 0.12 au and periods below 13 days. The shortest period binary has a $0.9M_{\odot}$ primary with a period of 2.25 days. Nevertheless, the authors concede that these binaries may have been hardened by close third-body encounters.

Morales-Calderon et al. (2012) pursued a different approach; performing photometric monitoring in the infrared to search for eclipsing binaries in the very young Orion Nebula cluster (age about 2 Ma). They found six binaries with periods between 3.9 and 20.5 days.

There are then quite a few other individual results and studies. I can't immediately locate any good compilation, but this is the closest binary that a brief search uncovered: Bakis et al. (2011) analysed the binary IM Mon, probably a 10 Ma old system in Orion. They find an orbital period of only 1.19 days and primary and secondary masses of 5.5 and 3.3$M_{\odot}$. Their radii are about 30% of the separation between the stellar centres (estimated to be $a=9.77R_{\odot} = 0.045$ au). The comparative youth and mass of this binary suggest it was probably "born this way".