The best way of paying for infrastructure like transit, is through "land value taxation."
There is good evidence that all warranted infrastructure (hospitals, transit, parks,...) could pay for itself if the rise in local land values that the infrastructure generated was collected by government for this purpose.
However, under the current municipal tax structure, most of the increase in land value is capitalized into the land, and therefore doesn't go back to the public purse which created it, but instead into the pockets of local land owners when they rent or sell their land.