How long does it take you to get from never seeing a sheet before to playing at the recommended tempo? Just wondering what’s typical.

It typically takes me several weeks at a minimum, with the caveats that I have little time for practice and am self-taught because I don’t have money for a teacher.

My process is this: practice each hand independently in chunks, bring each hand up to the ‘normal’ tempo, then put the hands together at sloooow tempo and gradually raise the tempo. The last part takes the longest. Does anyone have suggestions for improving my process?