Trying to avoid burdening my last comment, there’s also a technique called native chemical ligation that can allow you to make full length proteins semi-synthetically: part of the protein is made in cells, part of it is made synthetically, then the two are stitched together. This relies on peptides called inteins that naturally cleave themselves from pro-peptides. It relies on a cysteine to act as a nucleophile and can splice two sections into a new polypeptide. So under the right conditions if you have one peptide with an intein and another with a terminal cysteine you can get them to link up. There are still some real limitations - it’s easiest when the synthetic part goes at the end so you don’t have to sandwich it with two different reactions. You also need to have a cysteine in the vicinity or be able to make a mutant that tolerates the substitution. And, as others have noted, you still have to be able to get it to fold, which is often not trivial.