It's not a very typical path to enter MBB from industry unless you enter as a subject-matter-expert (SMEs at McKinsey or equivalents elsewhere). There are a few ways this can be achieved:
1. MBA: get into a 1-yr program if you don't want to spend 2 yrs (e.g. UK has a few great ones). Apply via school, interview, etc.
2. Contacts: if you know someone willing to vouch for you at MBB, go for it! You'll need to match this with recruiting cycles though.
3. SME route: the above two are typical for Associate level roles, but outside of that you may try the SME route ( more popular with MBBs lately).
I would never ask anyone to leave their job to do case practice. It's like asking someone to move out of their home in hopes of moving into a mansion. People in MBA programs (14hrs/day work-weeks) find time to practice cases, so you can too :)