Fox Park in itself isn't nearly big enough to support a cougar, but it's got enough wooded connections that I don't particularly doubt the report. A cat would have to cross interstate 95, but that's about the only real obstacle, and there are several underpasses. Many years ago a moose made it to Newton, so it's possible. There are plenty of deer nearby, though I don't think I've ever seen one within Waltham.
Since Covid, some Boston-area wildlife has gotten bolder. When Harvard was closed, a flock of turkeys took up residence in Harvard Square and hung around for months after people returned -- I haven't been by lately, for all I know they're still there. Sightings of coyote have multiplied all along the Charles, even in crowded areas. One was hanging out on the Harvard athletic fields in broad daylight during the Head of the Charles regatta.
At 150' in the dark, there's a chance it was a coyote in Fox Park - that would have been remarkable just a few years ago, but not so rare any more.