You'd definitely want to narrow down what you mean by "self-taught software engineer". Once you've done that, you'll have much more clarity in regards to whether it can be done in a year.

E.g., writing crud apps WebApps in Go? Definitely possible in a year. However, building a robust compute system in C++ from scratch -- probably not so much (for someone new to the field).

So just define what "self-taught software engineer" means to you, more accurately.