We are all currently traveling through time, though at a forward rate of 1 second per second (within your stationary frame of reference, since time dilation is a thing). But I take that you mean “time travel” as in advancing into the future at a faster rate, or going into the past.

In both cases, we do currently have the means of hermetically-sealed transportation. This is how, I believe, moon samples were collected in the mid 20th Century, since there was a possibility that alien life would be contagious to humans or that humans would destroy any samples of alien life. I think Tom Scott or someone did a video on the topic.

So while the biological risk would complicate time travel and visiting other humans, that alone doesn’t make time travel “impossible” because we could just have the travelers stay in their TARDIS or whatever. Like how people signed wills in 2020 atop automobile hoods.

There are plenty of other reasons why time travel is impossible though.