Those protein capsids must be pretty tough.
So at least the early stage of DNA entry is a passive process; just relies on good old force.
This is the same way, and with a similar degree of pressure, that the bacterial viruses called bacteriophage, inject their genetic material through the much stronger cell wall and into a bacterium.
Big fleas have little fleas,
Upon their backs to bite 'em,
And little fleas have lesser fleas,
and so, ad infinitum.
And the great fleas, themselves, in turn
Have greater fleas to go on;
While these again have greater still,
And greater still, and so on.
"The Siphonaptera", from Wikipedia