Yes, you can use it free for as long as you like. Airtable doesn’t limit you based on time, it limits you based on records in a base (total number of rows in all tables of a base).
The record limit for a free account is 1500, which should be more than enough to get started. If you can manage to recruit some friends to use Airtable by sending them promo invites from Airtable, you can earn credits towards paying for more storage.
And even if you go over your limits at some point, you will not lose any data. Airtable doesn’t delete any of your records, they just block you from adding any more to that base.