There are at least three known ways in which polystrate fossil trees occur. One is happening right now on the bottom of Spirit Lake at Mount Saint Helens in Washington state: thousands of trees sank to the bottom weighted by rock and hard soil trapped in their root balls, so they remain upright on landing. These trees will not rot because the water they are in is too deep and cold, and can easily last tens of thousands of years in that condition. They are slowly being buried in layers of sediment as they stand upright on the bottom. Since the water is mineral-dense, they are also slowly being petrified.
That’s the means I’m familiar with because some of my geology professors when I was at university studied them and continue to do so.
They don’t “wait to become fossilized”, they are being fossilized as they slowly – usually in a few thousand years – get buried because of the conditions they are in.
More interesting to me are the trees that get surrounded by lava and only get scorched, then at a later time when they are dead and dry a later lava flow sets them on fire and reduces them to ash while the lava that touches them hardens on contact, resulting in a tree-shaped hollow reaching through several lava flows.