Yes, a creature can move through the space
The hand is definitely not a creature
Spells that summon or create creatures consistently say that they summon or create creatures, and define the AC and hp of the creatures that appear - for examples see (find familiar (conjuration), phantom steed (illusion), animate dead (necromancy), and animate objects (transmutation). Maximillian's Earthen Grasp does neither of these things for the hand that it produces, so we can be confident that the hand is not a creature.
Moving through the Hand's square
A size Medium object in a 5' square might reasonably be considered to restrict movement as difficult terrain. However, I don't think the Hand is an object1 and while a DM could certainly treat the square as difficult terrain, I would not be inclined to do so on the principle of 'spells do (only) what they say they do'. Spells like Mold Earth say that they can cause difficult terrain, spells like entangle, web, spike growth, black tentacles, etc. say that they do cause difficult terrain. Ascribing that ability to a spell that does not specifically call for it is for me an unwarranted expansion of its power.
If the hand is neither a creature, nor an object, nor difficult terrain, then there is nothing that would restrict a creature from moving through its space.
So what's the deal with it being size Medium?
This is a bit perplexing. Looking through the PHB, all of the uses of a size category are for objects and creatures, not spells (spell effects have their dimensions delimited). It is not clear why the spell specifies that the hand is Size Medium. Although the OP and Eddymage suggest this is to determine the reach of the hand, that size category is completely unnecessary (or redundant), since the spell specifies that it may attack anyone "within 5 feet of it". While it is possible that the category is there because the intent of the spell is that it is an object1, I find it more likely that the size listing is an artifact of incomplete editing, and that it was introduced to an earlier draft of the spell that was intended to be an object, or was intended to grapple rather than restrain, but was later not removed as the spell evolved. In either of these cases (object or grappler) the size category would have mattered, but it currently does not.
1The hand is probably not an object
Unfortunately, spells that create objects are not so consistently formatted. Some spells that make objects tell us that the things they make are objects, and assign those objects an AC and hp; for example, Arcane Hand (evocation). Some spells that create objects tell us that they create objects, but don't define the AC and hp of those objects; for example Creation (illusion) and Fabricate (transmutation). And some spells that probably make objects neither tell us that what they make are objects, nor assign them AC and hp. For example, the food created by Create Food and Water is probably a set of objects, but the spell does not specifically say so.
Thus, the hand certainly could be an object - the spell tells us its size (Medium) and composition (compacted soil), so we know enough to assign it an AC and hp if we wish to treat it as an object.
However, I don't think it is, for multiple reasons. First, under 'spells do (only) what they say they do', the spell description explains how to escape it - a Strength check. No mention is made of being able to escape it by doing damage, unlike Arcane Hand for example. Second, the definition of an object is "a discrete, inanimate item", and the hand is certainly not inanimate (of course, neither is an Arcane Hand, but at least there the description states both that it is animate and is an object, so specific over general). Third, it is a transmutation spell. The transmutation school "modif[ies] energy and matter", but does not create it out of nothing, unlike conjuration, illusion, or evocation. When transmutation spells result in creatures (like animate objects) or objects (like fabricate), they make it clear that they are not creating these things but rather transforming them from other things already on hand. In the case of Maximillian's Earthen Grasp, the spell specifies both that the hand must begin on the ground and that it is composed of compacted soil. I think the spell can thus be best thought of as an animating force which is collecting the soil from the ground, compacting it (and transforming it when necessary, for example if the ground is stone), and arranging the soil as a mobile hand. The hand might be struck and disrupted, but then the force of the spell would instantly reform it from the material dispersed (and it is thus not 'discrete', either, another part of the definition of an object). This perspective is also born out by the way it moves - it must form in an unoccupied square, must move to an unoccupied square, but nothing restricts it from moving through occupied squares, although it can't do so and still hold on to a creature it is grasping. I imagine this as it moving more as a loose pile of earth that can flow around creatures and obstructions, but collects together and compacts itself in order to grasp a creature. When a creature moves through a space containing the hand, I imagine the hand would either be simply avoided or at worst, one could kick through the loose pile of soil and have it reform behind.
This is interpretive, of course, and if a DM wishes to rule that the hand is an object, that does not contradict RAW. But I believe the preponderance of textural evidence in the spell description suggests that it is not.