Welcome to the Airtable community!
The record limits in Airtable are soft limits, not hard limits.
I have had several bases go temporarily over limits and it has sometimes taken me a while to bring the number of records down. I have not lost any data due to being over record limits.
Note however, if you stay over record limits for an extended period of time, you might experience a loss of functionality, such as being unable to create new records…
In any case, you will need to look into techniques for bringing your record count down. A common method is to duplicate the base into an archive copy, then delete old records that you do no longer need in your day-to-day operations.