Ally McCoist's side booked a place in the last 16 with a 3-0 win over Elgin at Ibrox yesterday, when Kyle netted his first goal in front of the home crowd.
The Gers beat Motherwell before being knocked out of the Scottish Communities League Cup by Inverness Caley Thistle earlier this term.
Now Kyle is keen to embark on a remarkable run.
He said: "I believe we are [good enough to win the Scottish Cup].
"We showed against Motherwell in the League Cup how good we are.
"We turned them over and then it was the opposite against Inverness – they turned us over. It is just a confidence thing.
"As the weeks are progressing, we are getting better.
"We are getting players back from injury and have got a better squad.
"The manager has a bit of a headache picking subs.
"We have a good enough squad. We have to keep our league form good then make sure we turn up on the day in the cups.
"If we do that, we are capable of challenging anyone.
"When you see some of the results at the moment, anyone is there for the taking.
"The gaffer set out his targets at the start of the season. One was to have a good run in the cups.
"In the League Cup, we were disappointed to get knocked out and the Challenge Cup as well.
"The Scottish Cup is a big one, we are into the next round and we will take whoever we get."