Um amino acids don't get you life. Life is things replicating and amino acids and peptides made from them do not replicate.
The best handle we have on how replicators got started is the RNA World Hypothesis. RNA strings can be both information store and enzyme. So RNA strings can replicate themselves or get together with others to do replication. Proteins made from amino acids only come in later. Possibly even after DNA began to be used as the more stable information store.
Both the RNA polymerase complex which reads DNA into RNA and the ribosome which reads RNA strings to make proteins are largely made of RNAs. If you take the modern ribosome and strip out all the protein components and some of the more modern RNAs what you have left still makes protein. It is slow and buggy but it works and buggy can have advantages in exploring morphospace in terms of functional variants. Remember some of our genes can be read in different ways (paragraph skipping) producing different variant proteins even today.
But the RNA only ribosome tells how you bootstrap from a world of RNA replicators to one with proteins as well. RNA may be able to be enzymes but proteins can do far, far more in the enzyme and structural world.
At what stage did all this get enclosed in a membrane? were not sure but it could have been after proteins. Think pores in black smokers at the mid ocean ridges It's been calculated that temp differences in the pores could act like a PCR machine.
Today rna strings are very vulnerable in the environment, our fingertips drip rnases all the time. To work with RNA in the lab you MUST wear gloves. Which is why Covid-19 wraps itself in a membrane. Yes it's an RNA virus.