Yes, so basically you have 2 options to do this. The first is purely chemical using eg temperature and pressure. The problem is that when doing this method you get a lot of throughput but little control on direction the amino acid is added basicly you add v and v together and sometimes you get vv and the other x% of time you get v^. The problem here is that both react differently. Especially as proteins compose as little as 10 amino acids to thousands it can add up.

The second method is to use enzymes (other proteins) to create new proteins. This is actually what most living organisms including bacteria and humans use to make new proteins. It has the benefit of reducing the needed temperature and pressure while also often ligating amino acids in thesame direction. To make this easier we mostly let other bacteria such as E. Coli make those proteins by cloning the gene (DNA) for that protein into the bacteria and letting it produce it in larger quantities. This proces is often referred to as fermentation. The other, more expensive process is biokatalysis where instead of using an organism you use seperate enzymes in sequential order to synthesise your protein. This is usable for smaller/less complex proteins.