You can always build them up from scratch; with enough energy you can just get hydrogen from water and carbon from pretty much anywhere and synthesize whatever you want.
This isn’t energy efficient *at all* but, if we’re out of oil, then we’ve either sorted out alternative energy sources and have a lot of renewable power available or lack of plastic is the least of our problems.
There are lots of interim options though…organic chemists are very clever. As long as you have some kind of hydrocarbon feedstock (and tons of plants make those) you can eventually get to almost anything you want.
Edit:typo
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