Your DM will rule on this
The space rules for combat are silent on creature height, they only talk about two-dimensional floor space (p. 191, PHB). That means, any ruling on vertical extension will require your DM to decide how they handle it. Tasha's Cauldron of Everything, p. 4:
When you encounter something that the rules don't cover or if you're unsure how to interpret a rule, the DM decides how to proceed.
How could a ruling look like?
The DMG does provide some guidance on approximate humanoid creature size on page 248, making Large humanoids about 10 feet tall, and huge ones about 20 feet. Individual monster descriptions may differ; different giant races for example are all Huge, but range in how tall they are from 16 feet to 26 feet.
Wall of Force's dome option has these dimensions:
You can form it into a hemispherical dome or a sphere with a radius of up to 10 feet (...) If the wall cuts through a creature's space when it appears, the creature is pushed to one side of the wall (your choice which side)
So as a dome, it would cover 10 feet of height.
For a Large creature, it would cover nearly all of the creature's height, just leaving a narrow rim at the bottom. That could make it very hard for the creature to effectively fight back. To give you an example from our experience: we had a fight with Large demons that lacked ranged attacks and teleportation. We cast a wall cutting them off and leaving only a narrow slit at the bottom, which allowed us to pick them off with missile fire at leisure, turning what would have been a deadly fight into a risk-free slaughter. We as players of course reveled in our success with the tactic, as a one time event. (I could imagine it gets old if it happens too often).
For a Huge creature, the dome might cover only about half of its height. If you apply the squeezing rules (p. 192, PHB) to vertical dimensions, the monster should be able to move out from under it, unless you have it circled.
Squeezing into a Smaller Space
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 it remains in its space, the DM might let it attack normally -- after all, all of you are in the lower half of its space, where there is no dome in the way, and nothing blocking its strikes --, or they could give it disadvantage on its attacks, for example if they are using a club and the attack motion typically might involve swinging it over their head, or grant you half cover for +2 to AC. It is really their call.
