The Bills returned to practice on Thursday for the first time since Monday's game against the Cincinnati Bengals was suspended mid-game after Hamlin collapsed having suffered a cardiac arrest on the field.
Hamlin had to be resuscitated on the field and has been in intensive care in hospital in a critical condition since, but the Bills provided a medical update stating he was showing "remarkable improvement" on Thursday.
Hamlin's father Mario spoke to the Bills players and insisted that he and his son want them to play on Sunday.
"He didn't tell us, he demanded us," Allen told reporters. "You can't not honour his request to go out there and charge forward to the best of our abilities.
"Obviously, we'll be playing with less heavy hearts now, knowing that today's news was a lot of tears of joy. To know that's what he wants and that's what his dad wants, I think guys are excited to get out there."
Allen said "I do" when asked if he believed the Bills' players would be ready to take to the field on Sunday as scheduled.
"For every person it's going to be a little different. Putting that helmet back on today was really good for our team to go through that progress," Allen said.
"Some people are going to be changed forever after being on that field and feeling those emotions. The updates that we keep getting on Damar are lifting our spirits. Leaning on each other. We've had some open, honest and deep talks.
"We've had some unbelievable embraces as men, just hugging somebody, you need every bit of it. The fact we keep hearing good news about Damar keeps pushing us forward."
Allen conceded it would be difficult not to let the Hamlin situation enter his mind when they enter the field on Sunday, but insisted they had to shut it out.
"It's hard not to let it creep into your mind," he said. "We've been reassured this is the freakiest of freak accidents.
"The mental aspect of it, going out on that field, if you have that thought, that's putting yourself at risk even more.
"Coach [Sean McDermott] has done a great job making sure guys understand that and that mentally you need to be bought into.
"As humans, it's hard not to feel that way, but just to know the track record of the league. Obviously, there's injuries, that's part of sport and this is the worst possible case you can think of."