You can use thin-provisioned storage as one way to speed up initial sync times. Storage Replica queries for and automatically uses thin-provisioned storage, including nonclustered Storage Spaces, Hyper-V dynamic disks, and SAN LUNs. Once initial replication is initiated, the volume isn't able to shrink or be trimmed.
You can also use seeded data volumes to reduce bandwidth usage and in some instances synchronization time. Use the Seeded option in Failover Cluster Manager or New-SRPartnership to ensure that the destination volume has some subset of data from the primary site. If the volume is mostly empty, using seeded sync might reduce time and bandwidth usage. There are multiple ways to seed data, with varying degrees of efficacy:
Previous replication - by replicating with normal initial sync locally between nodes containing the disks and volumes, removing replication, shipping the destination disks elsewhere, then adding replication with the seeded option. This method is the most effective as Storage Replica guaranteed a block-copy mirror and the only thing to replicate is delta blocks.
Restored snapshot or restored snapshot-based backup - by restoring a volume-based snapshot onto the destination volume, there should be minimal differences in the block layout. This method is the next most effective as blocks are likely to match thanks to volume snapshots being mirror images.
Copied files - creating a new volume on the destination that wasn't used and performing a full robocopy /MIR tree copy of the data, there are likely to be block matches. Using Windows File Explorer or copying some portion of the tree doesn't create many block matches. Copying files manually is the least effective method of seeding.