There are schools beneath the pedigree you are seeking that have opportunities for Freshman and beyond. Not all kids want to do research and at many schools, if you ask a professor of interest, they will find you work in their lab or another. The departments also send out opportunities and some of them can’t find enough students.
If you want to do research, it’s likely not going to be an issue. And you won’t have to wait until the 3rd or 4th year to get interesting assignments.
And yes, if you’re at a T5 school that is feeding into high level institutions, that should be where you go as noted in many posts above - they will hopefully be able to give you the best guidance - although it’s always nice to get a third party bounce too.