DNS propagation

Hardly anything actually propagates. Your change is live at your authoritative nameserver as soon as the provider applies it, usually within seconds, though a provider running several authoritative servers can take a moment longer to have them all answering the same way. What you are then waiting on is thousands of recursive resolvers (your ISP, your office router, 1.1.1.1, 8.8.8.8) letting their cached copy of the old answer expire. The cache lifetime is the record's TTL, so a 3600 TTL means up to an hour of stragglers, and an 86400 TTL means up to a day.

The move: drop the TTL to 60 or 300 seconds a day before you plan to change anything, make the change, then raise it back. That way the old answer was already short-lived when you cut over. Check reality with 'dig yoursite.com' or a multi-location lookup site rather than trusting your own browser.

Two changes really are slower than your own TTL. Swapping nameservers is a delegation change, so the new delegation has to reach the parent zone's servers (the '.com' ones) on their schedule, not yours. And a lookup that failed before the record existed can be cached as a negative answer, governed by the zone's SOA, so a brand new subdomain sometimes stays broken for whoever checked too early.

Gotcha: your browser and OS cache DNS too, on top of the resolver, and Chrome keeps its own. 'Works for everyone but me' is usually a local cache or a stale HSTS/HTTPS redirect. The canned '24 to 48 hours' answer support gives you is mostly a stalling tactic inherited from the era of day-long TTLs.