SQL Server restore from transaction log
No. The recover process always starts from a full database backup and then it applies the log backups.

If your database has no backups then it is not in full recovery mode. Untill you actually take a backup it will always run in simple, no matter the intented recovery mode (aka 'pseudo simple', see New script: is that database REALLY in the FULL recovery mode?)

If your database really is in FULL recovery mode, then a backup was tacken and the recovery can start with that.

There are third party tools that can analyze the log and recover stuff, but they work only if the log was not recycled, so is back to the discussion whether the recovery model is really full or simple.