The use of the word "can" implies choice.

Any other time the word "can" appears in a ruling, it means that the thing is possible if you want.

Take the Combat rules for example:

On your turn, you can move a distance up to your speed and take one action.

You can forgo moving, taking an action, or doing anything at all on your turn.

You can take only one bonus action on your turn

Your turn can include a variety of flourishes that require neither your action nor your move.

You can communicate however you are able, through brief utterances and gestures, as you take your turn.

You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.

If you want to interact with a second object, you need to use your action. Some magic items and other special objects always require an action to use, as stated in their descriptions.

All these things are optional. You do not have to move up to your speed, but you can if you want. You do not have to forgo moving or taking an action, but you can if you want.

Note that it does not say "If you want to interact with a second object, you can use your action, it says you need to use your action. This is because there is no choice, you must use your action.

Leomund was a smart guy

Given Leomund's history, I don't think he would leave such a glaring oversight in his spell. It would make the spell largely redundant, as you could simply remove the earth under the hut and the occupants would walk through.

As shown in this article by Nerdarchy, Leomund was a smart guy. I don't really believe he would design a spell like this with such a large flaw in its design.

I would say the biggest reason Leomund is one of the famous wizards of distinction is because of his inventiveness. From the number of new spells he created to their utility in boosting the survivability of an adventure, Leomund had an answer.

I refuse to believe that such a clever and inventive Archmage would create a spell with such a simple flaw. I think he can design a working floor.

Conclusion

I would personally rule that the player can choose whether or not to pass through it, since the wording of the spell is in line with that and that would be best for my group. I also think it makes more logical sense if they are given the choice to pass through or not, since if you just passed through the bottom of the Hut, the floor is purposeless. There's no point to it if you have to phase through it and sit on the ground anyways.

TL;DR: Yes, they can pass through the floor if they want or they can choose to not pass through the floor and collide with it if they want.

However, I would also say that each DM should do whatever they think is the most fun for their group.

You Cannot Teleport Into the Tiny Hut

A key, though subtle point to this opinion is a statement on Range in the PHB (203)

Once a spell is cast, its effects aren’t limited by its range, unless the spell’s description says otherwise.

The suggestion is that during and before spell casting the spell's effects are limited by range.

Jeremy Crawford weighs in on this issue here, specifically in this tweet:

The indigo layer of prismatic wall prevents you from casting spells through it. This doesn't stop a spell with a range of self, such as misty step, but it does stop dimension door, which has a range of 500 ft.

and Leomund's Tiny Hut (PHB 254):

Spells and other magical effects can’t extend through the dome or be cast through it.

Because of it's range of 500 ft, casting Dimension Door to teleport into the Tiny Hut would involve casting the spell through the dome and cannot be done.