Tempo mapping - maintain groove - best method?

[Shazamm]

Hey all.

Wondering how to go about taking a demo recording - single audio file -
to have the grid match it -

I've done this before and it's a lot of hassle using identify beat for something recorded without a click to then adjust the tempo map- to tidy it up and tempo lock it

There must be another method using elastic audio and tempo mapping to work better?

And maintaining the groove btw*