What happened to Frodo, and also to Bilbo Baggins, is the usual exception that one is searching for in the rule: the two hobbits were not, by the way, elves nor were Maia, race to which Gandalf belonged, then branched into Istari. Among the Maia there was Sauron, before becoming the Dark Lord, and therefore, by absurdity, he too could reach Amar, to return to the lands originally created by Eru Iluvatar.
For Frodo, however, there was the approval of the Valar, who agreed to disembark him, Bilbo and Gandalf in exchange for their contribution to the destruction of the One Ring. Tolkien also mentioned a boat that crossed the whole of the Anduin Valley until it was lost beyond the Great Sea: Legolas, Gimli and Samvise Gamgee were on that ship, and in some ways, would have reached Aman in a second round as a thank-you to the work accomplished in the destruction of the Single, created by Sauron with the support of Celebrimbor’s knowledge. Overcoming the Great Sea was a practice that had been granted very few times, also because the separation of the continents was only around the end of the second era, just before the fall of the Dark Lord by Isildur’s hand, Numenor’s heir.
To create the Belegaer, the sea of Arda, was similarly Eru Iluvatar: before the huge expanse was completely icy and walkable, as did the Noldor fleeing from Valinor captains by Fingolfin and Feanor, the grandfather of Celebrimbror , which crossed the Great Sea, from Aman to Middle-earth. Afterwards, however, the war at Morgoth, which forced Eru Iluvatar to intervene to protect his elven children, the enormous expanse of ice opened and gave way to the infiltration of a large portion of Middle-earth, including Numenor and the Western Islands, including Tol Morwen, Tol Fuin and Himling. The strait was removed which allowed to walk the distance between the two lands and Aman was removed from the known world, brought to another dimension.
Although curvature suggests, Tolkien has never confirmed that the lands to the west of Belegaer would be lands east of Middle East, and that, in fact, a new way had been created to reach the lands where the few refugees numenous survivors. In any case, suppositions remain, in which we will not go to impelagare.
The birth of Valinor
Take the Dritta Road to Aman, a land that Tolkien had already described in Il Silmarillion when it was still to be reached on foot. It is a continent that in the far north was defended by the mountain range of the Monti Pelori, erected by Valinor.
The capital was Valimar, where most of the Vanyar and Maia resided, which, as explained, was the race that included Gandalf, Saruman and Sauron. In Aman there is where the Valar moved after the destruction by Melkor of their first dwelling, namely the Almaren lake in Middle-earth: here was founded the Valinor kingdom and all the geographic structure around it to cause it not to their home would be more attached.
Around the kingdom of Aman were created the Enchanted Islands, so called for the fact that anyone who had set foot on it would soon fall into a sleepy and eternal sleep. Despite all these defenses, however, Earendil managed to reach Aman.
