hotel · 3 tiers tracked · 1 free way in, 1 conditional
If you already carry the World of Hyatt Credit Card (Chase), you already have Discoverist — it's automatic for as long as you hold the card, no stay or application needed, and the card also throws in 5 tier-qualifying night credits a year toward whatever you're building beyond that. This is a US card, and it's the easiest way into Hyatt status by a wide margin.
The only other route in isn't free. American AAdvantage runs an ongoing Loyalty Point Rewards program that lets Platinum members redeem accumulated Loyalty Points for Hyatt status as a milestone reward, and roughly 100,000 Loyalty Points gets you Discoverist. Holding AAdvantage Platinum alone doesn't do it — you have to actually earn the points threshold, which makes this a much slower play than just picking up the Hyatt card.
There's no listed free or match path to Explorist or Globalist. If you want past Discoverist, the card's night credits are a start, but the higher tiers come from earning them the regular way rather than through a status match or a card perk.