Their invasion of Falme came as a complete surprise, but why? Did nobody try to cross the seas and come back again? No information from the Atha'an Miere (the Sea Folk)? Surely they had some contact with them?
I apologize for an incomplete answer, but I only can answer part of this.
The boats that Luthair Paendrag Mondwin was given by his father were specially commissioned to have a vastly different quality than the Sea Folk ships.
We need to go into some deep history I'm only tangentially acquainted with. The Sea Folk were content to stay near shorelines after they first saw the Isle of the Madmen and any who neared those shores were sunk sometime around the Trolloc Wars when the Sea Folk were looking for safer shores. Prior to that there are some sources that the continent of Seanchan was in fact found and there was some small trading, but the female channelers there had been twisted with power and were not deemed safe for their Windfinders to be near. This is how Artur Hawkwing knew there was another continent to send his son to. And that his son would need an army.
Once the armada had crossed the Aryth Ocean, Mondwin knew he was alone and started to conquer Seanchan, which was still very barbaric and had none of the stability that the White Tower had accomplished in the Westlands, small warring tribes and attempts at nations that were quickly taken over clearly did not have the technology to create ships that would make it across the Aryth.
As to why the Seanchan took too long Mondwhin had insisted that all of Seanchan be captured before they Returned to the Westlands, not wanting to disappoint his fathers legacy. Unfortunately this took a little over a millenia before they were finally able to establish the entire Empire of Seanchan.
EDIT: Totally forgot to obvious part of the question. After Mondwin never returned and no one came after him, it was assumed that they had all sailed to their death and there was no country or individual with resources to send a better supplied or even equally supplied fleet to see what had happened.