Should I update Serial on SOA when migrating DNS for my domain

I'm in the middle of moving DNS for a personal domain from a legacy hosting provider to AWS Route 53.

Old SOA record on the old hosting provider's DNS:

    serial  = 121040502
    refresh = 10800 (3 hours)
    retry   = 3600 (1 hour)
    expire  = 604800 (7 days)
    default TTL = 3600 (1 hour)

As it's created on AWS for the hosted zone:

    serial  = 1
    refresh = 7200 (2 hours)
    retry   = 900 (15 mins)
    expire  = 1209600 (14 days)
    default TTL = 86400 (1 day)

As you can see, serial on AWS is 1 vs 121040502 on the old DNS.

Should I alter the SOA record on AWS such that "serial" is higher than the previous server?

The serial doesn't really matter if there are no nameservers doing zone transfers.
(To my knowledge Route53 does not support transfers in either direction, so it seems like a safe bet based on your question)

The SOA serial number is only relevant when your secondary authoritative name servers rely on zone transfers from the primary authoritative name server for the replication of zone data. Then after each change the serial must be incremented for the secondary to be aware of the update to the zone data.

When you are completely changing from your existing name servers to new ones and/or a new provider, the old SOA serial value is irrelevant. Even if the new provider actually still uses zone transfers for replication, you start there with a clean slate with regards to replication.

Using 1 as the initial SOA serial in a new zone is perfectly fine.

Since AFAIK Route53 doesn't rely on zone transfers, you probably don't have to change the SOA serial number ever again for any immediate technical reasons