Problem with oil change

You need the correct tools for a start, and an ordinary allen key/hex key won't do it. You need the correct one on a ratchet or similar to give you the leverage to open it.

Your photo isn't great but it doesn't look too bad. When you have the correct size tool in the correct potion, I'd give it a tap of a hammer to seat it in as much as possible before opening.

Is this the first time the car will have had an oil change under your ownership?

It looks like whoever did a previous oil change didn't have the correct tools for the job either, but ploughed on regardless

Either way, I'd be looking for a new sump plug, as that will just break your heart down the line…

get a replacement plug, and the correct Allen socket that fits to open/close it. Then carefully remove/destructively remove the old one.

Failing all else put a chisel/flathead screwdriver perpendicular on the edge of the bolt and hammer it untill it makes a cut, then put an angle on the chisel or screwdriver, and hammer it from there, should loosen it. If you have time go buy rounded hex remover bits.

Either way it needs a new drain bolt.

If you don't want to use a vacuum pump then you can replace the sump plug (if you get it out!) with this device. Once you have it installed you are finished with the requirement to use any tool for ever more. Has a built in 'non return valve'. You just screw off the cap and plug in the hose with the special fitting.

Ignore every other suggestion. Tap a spline into it.

Standard mechanics solution.

That's a destroyed sump along with a mangled nut. The OP needs to bring the car to a garage and get the sump nut replaced, then they can buy a vacuum pump and do their own maintenance in future.

The fact that they are asking shows that they don't have the skill to fix the problem. No harm in trying to do DIY maintenance but sometimes you have to let the professionals fix the problem.

Of course heat worth a try but not too much as near sensor

No to hammer and chisel as the sump is thin.

New sump bung and washer/seal.

No to that oil drain valve or you risk ripping it off the sump as bung will protrude and might take a knock.

Size wise bung looks smaller than 12 ? Always had many 17 , 14 ,12 , 10 ,8 , 7 , 6 sockets

Google tool needed for your sump bung as might give a size.

It's probably not that tight so - just not getting purchase on it.

If you drained the sump with a pump, you could drill it, and then use a damage bolt extractor, but expect a mess. I'd still tray and hammer in a torx or spline bit.

Vacuum pump only 15-20€ lidl or Aldi and you can use it on your next car

Used my Lidl one for years with no problem, 1st time I used it I pulled the sump plug and not a drop of oil came out.

I've used it on a Tucson and a duster and an I10

Agreed, get a pump, but some are better than others. I have the free standing type with a handle that you push down. It takes about a minute to suck a few litres of oil out of the dipstick hole. About 70 euros on amazon.de. That is assuming that the car has a dipstick or other hole to extract the oil from.

Alternatively, the OP can fart around with chisels, hammers, splines, welders and blowtorchcs (what could possibly go wrong there in the vicinity of a pan of oil) Or else pay a garage to loosen the nut and change the oil. They won't have much change out of 70 euros labour for that. Also, sucking ou the oil and leaving the drain plug in situ is exactly what a garage would want to do unless instructed otherwise.