Achiral universe - asymmetric synthesis
Yes! There is a simple possibility. Take one racemate and do what Pasteur did:


be lucky, in that both enantiomers crystallise separately;
be lucky again in that they form macroscopically distinguishable crystals (in this case probably: mirror images);
collect the different enantiomers. Voilà, you have enantiopure substances and can use them in synthesis.


(Thankfully, using tartaric acid immediately gives access to the Sharpless asymmetric epoxidation.)

Once you have any single enantiopure compound, you are able to generate further ones. For example, reacting a racemate with an enantiopure compound in a way that preserves the respective stereocentres will result in diastereomeric products. Diastereomers can theoretically always be separated (it may be harder for some and some may interconvert under ambient conditions but the theory stands). You could also generate diastereomeric salts, by taking an enantiopure anion (say (R)), and a racemic cation. You will receive the diastereomers (R,S) and (R,R) which can then be separated and so on and so forth.