NO, but it depends on your world setting
In the spell description of Mirage Arcane (PHB p.260) is says that "You can make terrain in an area up to 1 mile square look, sound, smell, and even feel like some other sort of terrain." There is a clue in some other sort of terrain. If your world setting has an environment or terrain in which stone/earth is actually transparent or translucent, then I would say "yes" this works. If your world does not naturally contain that setting, I would say "no" for that same reason.
Also, the 4th level spell Hallucinatory Terrain (PHB p.249) gives a further clue as it contains a lot of similar features. So, in theory, if you allow Mirage Arcane to modify terrain in such a way, you also would need to do it for Hallucinatory Terrain because what was suggested is modifying the "look" of the terrain. The area of effect is less, but it would still be unbalanced.
If we consider the magic item Ring of X-ray Vision (DMG p.193), a rare item that permits a wearer to see through only 1 foot of stone among other things, we can get a further clue. We can create our own magic items as DM's and there is some guidance in in the DMG (p.285). It suggests the maximum level of a spell to determine rarity; for rare items it is 6th level and for uncommon items it is 3rd level. Although there is not x-ray vision spell in 5e, we could suppose from the rarity of this item that, if there were such a spell, it would likely be a 4th-6th level spell. Now, this would only confer sight of seeing through 1 foot of stone. Where as if you allowed Hallucinatory Terrain to be used in this way, you potentially allow a 4th level spell to see through 300 feet of stone/rock/earth. It would be definitely unbalanced.
For example, say you set an adventure in a cave system where you have hidden enemies, traps, secret doors/passages and and you've hidden an incredibly rare artifact... Then, your clever wizard thinks: "Oh I know I will cast Mirage Arcane and make the whole cave system transparent, like I did that time with the vampires." Two minutes later: "Hey guys, I dodged all the mobs and look! I found the incredibly rare, super hidden, almost impossible to find artifact: The One Ring." (Sorry about the LoTR reference, but I couldn't resist.)
In the example the intention of making all stone/earth transparent or translucent so as to allow sunshine to pass through, it is not really about creating an illusion, but about modifying the properties of existing geological structures - which is quite different. This is more the field of transmutation spells.
I might allow it as a one-off as Rules as Fun, but I would have to think about it in terms of where my campaign is heading. There is definite danger of this strategy being over-used and abused in future sessions. So, in general I would say no.
It is worth remembering that there are many D&D campaigns that have substantive outdoor adventures, and allowing this use of the spell may ruin many settings and adventures.
I hope this helps.