The kingdom itself existed for nearly 200 years and was the major Crusader State of that period.
There's a chance that the Ottomans may have too many diplomatic relations by the time you're able to get them to support your independence, in that case, restart the game or rollback to a previous save. Has unique content without Golden Century. Instead if the player is playing as Cyprus, The Knights or Provence they will reform into them and be able to play as them for the rest of the game.
This will allow you to make use of the Crusader mission 'Crusader Fleet' to get a free and permanent claim on the Palestine area.
If the player has taken care of building a stronger army and navy than their target, the player should have no problem taking the island, which can then be used as a base to forge claims on two of the three needed provinces (the Ottomans are unlikely to take those provinces during their first war with the Mamluks).