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Not into Penn; too many buildings in the way, and the grades would be very steep. The open cut between Ninth and Tenth Avenues has been built over, too.

IIRC, the coast guard requires a bridge over the Hudson River to be 230 feet above the high water mark. That’s for accommodating cruise ships such as the Queen Mary II ans suchlike.

There have been several studies over the decades (even centuries) into building a rail bridge from New Jersey into Manhattan (one example is this remarkable unbuilt proposal to join the Long Island RR’s Atlantic Avenue Branch to the Central RR of NJ and the Baltimore and Ohio at the Battery, and another unbuilt one from Hoboken that the Pennsylvania RR refused to participate in due to an absurd financial burden being asked of them in return for their participation), but the politics even over that span of time have been utterly absurd, including restrictions on steam locomotive operation in Manhattan.

Also, the lower level of the George Washington Bridge was originally intended to host railroad tracks, just as the lower level of the Oakland Bay Bridge in San Francisco used to carry electric trolleys and interurban trains.