The 20-year-old has been substitute keeper for the first team since the departure of Neil Sullivan to Chelsea and says he sometimes can hardly believe that he is second choice at a Premiership club.
"That's right, it only really sunk in for me at Arsenal - and that was after ten games," said Rob. "Even now I still don't just expect to be on the bench and half expect Lars Hirschfeld to come back in. It is a dream for me at the moment and I've got to keep going and work hard. Hopefully that will keep me in there.
Pushed gently, Rob does concede that when speculation began linking Sullivan with a move, he was wishing him towards the exit door.
"I was - I admit it," he laughed. "It is natural though. I knew Lars had a few knocks and I thought I was improving as well. I did well in pre-season and it was nice to get the chance.
The England under-20 international has just been rewarded for his efforts with a two-year contract extension and is grateful for the security provided by the new deal.
"It's nice for me, a couple of boys have been let go recently and it is good for me to know I've got a bit of security.
"I've been on the bench lately and it is a nice reward for me. I've worked hard in training to keep myself on the bench and that is important to me. I work hard in training and I can't afford to slip, if I do I don't think I'll stay as second keeper.
Rob makes light of the downside of being the back-up keeper - not getting to feature in that many games - and suggestions of a loan move to achieve that are swiftly dismissed.
"Oh no! That is the thing, I want games but I'm on the bench and I want to stay there as long as I can.
"With being on the bench I haven't played so much lately. Pat Holland said to me that I've got a reputation but I never play! It is true, but I played a lot in pre-season and was chucked in at the deep end and did okay."
While Rob is relishing his work with senior goalkeeping coach Hans Segers and Kasey Keller, he credits his Academy coach Perry Suckling for putting him on track to fulfil his dream of being a fully-fledged Premiership player.
"I keep saying it - if it wasn't for Perry I wouldn't be here now. I owe him and would love to do something for him in return, but I don't know what to do.
"He's done so much for me and we did so much hard work. If we had a day off he would come in and help me - I owe him everything."
Rob Burch admits it has only recently sunk in that he is currently No.2 goalkeeper at Tottenham.