Free will. Eru never compels creatures -- be they Valar or Hobbits -- to act other than according to their own choices. Even the Valar freely choose to submit to Eru's will -- Melkor fell precisely because he did not so choose.
Gandalf chose to be embodied and go to Middle-Earth and try to rouse (but not force) Men and Elves to resist Sauron. Aragorn chose a life of hardship with little hope to resist Sauron. Faramir and Galadriel chose to renounce the Ring when they had it in their grasp. The Hobbits chose to go off on a dangerous journey with little chance of success.
Likewise, Boromir and Denethor each chose to try to seize the Ring -- having been warned that that would be terribly dangerous and ultimately worse than futile -- to save Gondor. Saruman chose to turn away from his task to pursue power. Sauron and Melkor chose to selfishly pursue power over others.
Each of them had the free will to choose good or evil based on their own values, personalities, wisdom (or lack of wisdom), knowledge, motives -- in short, based on themselves.
Isildur took the same path as Boromir and Denethor and in spite of knowing the danger of the Ring, chose to keep it. For Eru to have tripped Isildur would have been to make a mockery of his free will.
Finally, in the Silmarillion, Eru says of Melkor's evil (but free) choices:
And thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined.'
In the end, even creatures' evil choices will result in a better creation.
Finally, did Eru trip Gollum? He certainly didn't do so 'on screen'. The story doesn't say and no one in the story knows. Gandalf certainly doesn't. OTOH, Gandalf certainly believes in what we call "providence" but he believes in it and doesn't know it for a fact. On another matters, he says to Frodo:
"...It was the strangest event in the whole history of the Ring so far: Bilbo's arrival just at that time, and putting his hand on it, blindly, in the dark.
'There was more than one power at work, Frodo. The Ring was trying to get back to its master. It had slipped from Isildur's hand and betrayed him; then when a chance came it caught poor Déagol, and he was murdered; and after that Gollum, and it had devoured him. It could make no further use of him: he was too small and mean; and as long as it stayed with him he would never leave his deep pool again. So now, when its master was awake once more and sending out his dark thought from Mirkwood, it abandoned Gollum. Only to be picked up by the most unlikely person imaginable: Bilbo from the Shire!
'Behind that there was something else at work, beyond any design of the Ring-maker. I can put it no plainer than by saying that Bilbo was meant to find the Ring, and not by its maker. In which case you also were meant to have it. And that maybe an encouraging thought.'
Gandalf is surmising -- he "can put it no plainer" because he doesn't know. He believes and he hopes, but he doesn't know.
Later addition: The whole matter of free will and providence is very subtle, and I think Tolkien understood that subtlety. Eru knew that Gollum would carry the Ring into the fire, but He didn't push Gollum: He didn't have to.
Gollum became Gollum as the consequence of a lifetime of bad choices deliberately made by Gollum (and by Smeagol before him.) Smeagol was captured almost instantaneously by the Ring and killed his friend Deagol to possess it. Had Smeagol been a different person, he might have resisted -- both Bilbo and Frodo did, after all. So did dozens of other people (Men Elves, Dwarves, and Hobbits) who knew of it and had an opportunity to seize it.
Gollum had turned himself into just the sort of person who would fight Frodo at the edge of the chasm at Mt Doom and who would be so enthralled by the Ring that he would disregard everything around him (including a hole filled with molten lava...) once he had it. Dancing in glee, oblivious, he fell.
Eru knew that would happen, but it still happened entirely as a consequence of choices made by Gollum based on his own personality, desires and experience. Gollum was no one's puppet. (If Eru did anything, he -- almost miraculously -- preserved Gollum until he could finally, by overreaching in a way completely in character, destroy the Ring.)