Can a character move a creature into an empty space that would require it to squeeze?

Page 192 of the Player’s Handbook has rules for squeezing:

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that’s only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it’s in the smaller space.

The Crusher feat from Tasha’s Cauldron of Everything allows a character to move a creature it hits with an attack that deals bludgeoning damage 5 feet to an unoccupied space:

[…] Once per turn, when you hit a creature with an attack that deals bludgeoning damage, you can move it 5 feet to an unoccupied space, provided the target is no more than one size larger than you. […]

Could a character move a creature it hits 5 feet to a space that the creature could otherwise only occupy by squeezing, and thus inflict upon that creature all the disadvantages that entails?