You are asking is it safe: Installing a NEMA 10-50 range socket. No, that is not safe. This was banned in 1996 because of the body count. The fact that yours was installed prior to 1996, and is thus "grandfathered", does not make it any safer.
When your installers say "it's safe", they mean "it's safe FOR THEM" because they won't be using your range. Also, appliance installers don't have an electrician's license at risk.
If your range does not require neutral, then it should be using a NEMA 6-50 plug. If the range does need neutral, then you are safer with a NEMA 14-50 type plug, and that would mean retrofitting ground to this socket. The ground must be #8 (for reasons) either back to the panel or back to a box which has #8 back to the panel, or has non-flexy metal conduit back to the panel.
Also, this is a goobed up mess.
The #2 problem is that a junction box can't just have a hole bashed in it by smashing a rock against it. The cable entering it needs to have a proper cable clamp, which means the box needs a proper knockout.
The cable is #4 SE cable, and that cable can do 2 interesting things: First, that bare wire actually does get to be a neutral wire. (or a ground, your choice). And second, it's good for 55A generally, but since it can run at 75 degrees C, we can actually get 65A out of this wire (but not going into that old 60°C panel; we'd have to pigtail to larger wire outside the panel).
Aluminum is fine at these large sizes, but only if the receptacle is rated to attach to aluminum wire! (remember; that's what caused all the trouble in the 1970s!) What's more, I would be very surprised if a 30A receptacle was rated for #4 wire, since it only needs #10 copper (or #8 aluminum if it accepted aluminum). So I am suspicious as to how the wires were attached to the NEMA 10-30 recep.
The size is #4. The size of the individual wire strands is irrelevant, as you cannot use the wires individually. At all. The only purpose of stranding is to increase the flexibility of the entire wire. You must not remove some strands to get a wire to fit a too-small connector.
If the receptacle is not rated for aluminum, or not rated for #4 wire, replace it with one that is. That shouldn't be hard with NEMA connectors.