What will happen if I don’t get my green card renewal process started before the expiration date?

You should try to file before it expires but it should not be a big deal if you do it a bit later.

It is recommended to start the renewal process 6 months before the green card expires. If for some reason you are unable to renew the card before it expires, you will not have valid proof of your immigration status which may affect your ability to maintain or find a new job.

If you were asking if after your green card(not conditional green card) expires you would lose your LPR status, you do not need to worry. You remain LPR regardless if your card is still valid. Just file the renewal when you have chance to avoid problems when you try to return to the US after a trip abroad. If your green card is conditional, then you must file within 90 days before it expires, although you can always file it after the 90 days window if you have good reason.

Nothing bad will happen to you just because your green card has expired. For instance, you do not lose your citizenship just because your passport has expired. Similarly, the fact that your green card has expired does not mean your status as a legal resident has expired. However, you should file to renew your green card [Form I-90] as soon as possible. A valid unexpired green card is the proof of your right to live and work in the United States.

No, it is not a problem. Your green card, which usually must be renewed every 10 years, is evidence of your permanent resident status, which never expires. You should go ahead and file for the renewal now, though, since a current green card is necessary for employment purposes and driver's license among other things.