You may want to pace up the shnapshot/ restore process by updating settings of your repository. For instance, if S3 is being used, there are some properties defined here: S3 repository | Elasticsearch Guide [8.6] | Elastic
Also, there are some properties that can be defined to pace up shard initialization as posted in this thread: Snapshot restore is very slow to get started - #7 by Guilherme_Vieira
and here: Snapshot is taking too long