
When he starts at 2.30am are you taking him our to toilet? he could be an exceptionally clean little mite who doesn't want to dirty near where he sleeps, or simply on waking when his bladder or bowels call, finding himself alone, and is frightened/lonely.
Quietly taking him out as soon as he starts, not paying him any attention other than giving him his toilet command and then back to bed.
do not interact or play with him, but wait for him to settle in his bed again ignoring him all the while. Put the kettle on, make a cup of tea but do not interact with him. he should wander off and lie back down. You then quietly go back to bed.
You may need to get up again about 5 or 6am to do the same. It is no different to a human baby.
As for paper that is just to mop up and should not be looked on as training, in fact having paper down that he gets into the habit of using will just teach him to go indoors.
The way to house-train is to watch him like a hawk when eh is awake, take him out at least every hour whilst awake, after every meal, game or drink.
You need to take him outside and use a word or phrase only used for toileting, and as soon as he performs praise and/or reward with a tidbit.
As a breeder in common with other breeders I will use paper with a litter to soak up what pups do when in their indoor pens when tiny. I may also put paper down if I have to leave a pup in the house and know where it is most likely to choose to go, to make cleaning up later easier.