The minimum price of existence involves reserving a server and 10GB of disk space (about $6/month). This cost is incurred if you leave it empty and do nothing with it the entire month. Serverless things typically can scale cost closer to zero if real usage reflects that.
CockroachDB and several companies offer a very competitive free 5GB postgres or almost postgres DB, some companies like fauna offer 5GB of suitable NoSQL, but most of them leap straight to $25/month to exceed the free tier. There's almost nobody out there who is offering to charge me less than a dollar per month if I only need less than a dollar worth of storage, read/write, bandwidth, open connections, etc.
