In short, yes, but not all proteins are equal here. Longer ones are harder to make.

There are techniques for immobilized substrate synthesis. Basically you glue you starting amino acids to a surface, and you wash your next amino acid reaction blend over to attach the first one. Rinse and repeat for your growing peptide.

This is great for smaller peptides, but massive biopeptides become another beast. G-mod yeast is another great tool as its a cheap way to make abunch of a target protein or enzyme. This is awesome if the enzyme you want already exists in nature.

But fully synthetic peptides? Especially enzymes? Very very very tricky. Some of the most powerful computational chemistry goes toward predicting how proteins will fold, and folding into the right shape is crucial. Fold into the wrong shape and you get Mad Cow Disease, for example, or most often just a dud.