Can I apply for EB3 after first year on H1b?

Hi I have been reading everywhere that backlog for Mexican Nationals is 6 years as of today. I just completed the first year on my H1b and I am thinking of applying for GC on EB3. My question is: How would it work if EB3 application is accepted will by H1b visa will still be valid until GC is granted ? could I save some time this way? I am aware that I might have to extend my H1B after the 6 year period. Please any ideas or inputs as what I want to do. Am I crazy for even thinking of starting EB3 on first year of H1B.?

Thank you so much!

Your employer can file GC even now. It will continue to get processed and will happen in parallel to your H-1. You will have to maintain H-1 status until your I-485 is filed (when you can either move to EAD or have AOS filed if dates are current).