There is no way to restore from a postgresql binary backup without WAL. Regardless of the backup software was used: pg_basebackup, pgbackrest, barman, wal-e, wal-g or something else that uses a binary copy of the data directory.
Even if case when a postgresql server was completely shut down while the backup was taken. It is mandatory to have WAL segments to start the database system.
So, if you have no backup (correct, a basebackup without WAL means no backup) and you want to start the database and damage your data - you could try to use pg_please_damage_my_database tool, also known as pg_resetwal. Please read the docs carefully. After that, any anomalies in the data are expected, for example, you may find duplicate rows under a unique constraint, see rows that have already been deleted, or cannot find recently added rows.
