Unfortunately, no - you also need to have a clear path to the target
Many spells do specify that you must be able to see a target in order to affect it, and mass cure wounds notably does not - so it's entirely possible to cast it on creatures that you can't see, so long as you are sure they are in the spell's area. Unfortunately for your scenario, though, there are more general rules about targeting spells and areas of effect which require a "clear path" to the caster or the point of origin, which in most cases rules out being able to affect a creature that has been swallowed by another creature with a spell like mass cure wounds.
In short: you need a clear path from you to the AoE origin, and from the AoE origin to the target, to be able to affect it with the spell - but the swallowing creature is an obstruction which blocks those clear paths, so you can't reach the swallowed victim with the spell.
From the basic rules on combat, total cover:
A target with total cover can't be targeted directly by an attack or a spell, although some spells can reach such a target by including it in an area of effect. A target has total cover if it is completely concealed by an obstacle.
From the basic rules on magic, spellcasting requires a clear path:
To target something, you must have a clear path to it, so it can't be behind total cover. If you place an area of effect at a point that you can't see and an obstruction, such as a wall, is between you and that point, the point of origin comes into being on the near side of that obstruction.
And about areas of effect:
A spell's effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn't included in the spell's area. To block one of these imaginary lines, an obstruction must provide total cover.
In conjunction, these rules state that you can't directly target something that has total cover from you, but you can still catch it in an area of effect, assuming you can place the point of origin of the AoE somewhere that does have a clear path to the target - which in turn requires you to have a clear path to the point of origin.
Mass cure wounds isn't a directly targeted spell, as it produces an area of effect - a 30ft. radius sphere - from which you may choose which creatures you'd like to affect, and it describes the "healing energy" of the spell as originating from the origin point of the AoE. Unlike certain other AoE spells such as fireball, the spell has no language allowing the AoE to spread around corners, so the normal rules requiring an unbroken straight line to the AoE's origin apply.
Being swallowed by a creature unfortunately means that the swallowed victim is in total cover relative to anything outside the swallowing creature - all creatures that have the swallow ability have similar text in their stat block that explicitly states so (at least, I'm not aware of any exceptions, though for a particularly unusual creature this might not hold true, at the DM's discretion). For instance, from the giant frog:
The swallowed target ... has total cover against attacks and other effects outside the frog
If the AoE's point of origin is outside the swallowing creature, the area cannot include the swallowed victim, since they have total cover from the point of origin. You can't be crafty and place the spell's point of origin inside the swallowing creature, either, because the creature's outside presents an obstruction to your clear path to its inside - if you tried, the AoE would just originate from a point on the surface of the creature instead, and still wouldn't reach the swallowed victim. Altogether, this prevents you from being able to affect a swallowed victim with cure mass wounds.
Of course, with a willing DM, you might be able to contrive some way to reach the unfortunate victim regardless - perhaps if you can poke a large enough hole in the swallowing creature to be able to target inside it, or time the spell's casting for a moment when you can see down the creature's mouth/throat. (As a last-ditch resort, being swallowed by the creature yourself would allow you to reach any other victims it had already swallowed.)