For the OP - I open up evap cases once every bunch of years to check a few things: That there is no mold growth, that the evap isn't becoming a rusty mess, and that the fins look reasonably clean (that dirt particularly fibrous matter isn't somehow bypassing my 4" thick filters).
I have furnaces in the attic with evaps that are A-coils that lay on their sides. Usually on those there is a panel that can be carefully removed by taking out sheet metal screws. That offers a side-on view of the "A".
From what I can tell of your first pic, the right side, from where the liquid and suction lines are placed (about half way up) plus what looks like the relative thinness of the evap case near-to-far (again, the pic is dark and not a good view of right side), I'm thinking you have an H-coil evap. An evap coil that was purpose-built for horizontal furnaces and horizontal air handlers. The H-coil evap's case is a band of steel that goes all the way around it, right, top, left, bottom.
As such, there is nothing that will come apart on the H-coil itself to see in when installed. Have to separate either the output end (the end towards the octopus of supply ducts off in the distance), or the input end (the return, which I figure is the big round flex duct in foreground of pic). It's possible that pulling all those sheet metal screws holding the return plenum end and return duct, would allow one to pull back the end of the return plenum (while compressing or bending flex duct back and forth like a snake). That should give room to look inside at the face of the evap H-coil.
I note that in the second pic, that I don't see the back of the evap's metalwork on the left side... looks like the sheet metal side goes on by. So maybe the whole assembly was built as a box, and the evap was slid in from the right and fastened down. With the way the refrigerant lines are run, you won't have slack to unfasten however the evap coil is held in, and slide it out to the right to inspect it. So if I was doing it, I would do a good visual to see how that front end cap is held on as I mentioned above, and pull that out to see straight in to the coil's face.
But you have other things to consider... with no plywood securely and safely fastened down with screws to the joists, you do not have a safe work platform. Also, there is the "maybe let sleeping dogs lie" unless you suspect some problem. I would think you could get somebody in to disassemble it enough to look at the H-coil, but it's not going to be a quick in and out job, maybe a job left for a slower time of year for A/C places.
If an evap coil is pretty dirty, there are aerosol cans of coil cleaner that can be used to spray them down, then spray them off with water. Being careful to keep water spray at such an angle and amount that it washes the dirt down into the evap's drain pan, and out the drain... without overloading the pan with too much water at once and have it overflow, or run all over inside the plenums.
The first pic is so dark and at an oblique angle, that you would really need to verify where the blower motor is, and which end is which, return (input) and supply (output), as I may have it reversed. Either way, to open up one end and see the coil, the blower motor can't be in the way, and you need to be within arm's reach of the evap coil to actually do anything inside.
If you don't know how, call someone that does otherwise you may be in for a shocking experience or worse. Remember caps can shock you even when the power is off.
