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I think both approaches work, but given it's May already I'd just give them the big pots now, so they build a proper root structure now - which they are going to need soon when it gets warm and they are starting to flower (which takes more energy than anything else in their life).
As far as I know moving them up gradually only makes proper sense if you're starting early with artificial light (and if you're doing a lot of plants - they just take up less space : )
See two posts above yours.
And yea, bigger pots now, and as much sun as possible.
Water only once the soil goes dry-ish below the surface.