PostgreSQL PITR - more doubts

Hello all,
One doubt about how PostgreSQL PITR works. Let us say I have all the
archived WALs for the past week with
archive_command = 'cp -i %p /home/postgres/archive/%f </dev/null'
I took a base backup last night. If I try to recover the server today
after
copying the base backup from yesterday and providing
restore_command = 'cp /home/postgres/archive/%f %p'
does PostgreSQL go through all the past week's archived WALS or
it can figure out that the base backup is from yesterday, so skip
a large number of archived WALs and start only from file xxx ?
Either way, are there ways to speed up the restore process?
Regards,
Jayadevan

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