The trio were named on Tuesday for matches in Darwin (Aug. 13-17) and Mackay (Aug. 22-26), which form part of the World Test Championship cycle, after playing only three tests between them during the Ashes in the last home summer.
Australia's "big four" of Cummins, Hazlewood, Mitchell Starc and Lyon have not bowled together since the West Indies tour a year ago due to various injuries but chief selector George Bailey said it was too early to confirm whether they would all turn out against Bangladesh, despite being fit.
"We won't be locking in an 11 this far out," Bailey told reporters in a video call on Tuesday.
"We do know that across this two-test series, the depth is there."
With 295 test wickets at an average of 24.21, 35-year-old Hazlewood has been one of Australia's most devastating bowlers but injuries have limited his output in recent years, including forcing him to miss the entire Ashes series with hamstring and Achilles problems.
In his absence, 37-year-old seamer Scott Boland took 20 wickets in an excellent series in the 4-1 defeat of England, and Bailey was frank about the competition Hazlewood faces from the Victoria quick.
"Scotty would never say it, but yeah, I think he's mounting a strong case that when you use the words of big three (fast bowlers), that he could be one of those," said Bailey.
Hazlewood's recall means no place for Michael Neser despite the paceman's fine Ashes campaign.
The squad is the first following opener Usman Khawaja's retirement, potentially creating opportunity at the top of the order.
South Australia opener Jake Weatherald has been retained despite struggling during his debut test series in the Ashes when he averaged 22.33 across the five matches.
The pocket-sized lefthander has yet to convince but Bailey said selectors saw positives in the opening combination with Travis Head during the Ashes.
"Hopefully we do see some growth out of that (Ashes) and some understanding of what it takes for success at test level," he said.
Cameron Green has also held onto his spot after a disappointing Ashes with bat and ball, and is one of two all-rounders in the squad with Beau Webster.
Josh Inglis was retained as a potential middle order batting option.
Australia sit top of the World Test Championship table midway through the cycle and will look to cement their place with a series win over fourth-placed Bangladesh ahead of a tough tour of South Africa in October.
Australia 13-man first Test squad:
Pat Cummins (c), Scott Boland, Alex Carey (wk), Cameron Green, Travis Head, Josh Inglis (wk), Marnus Labuschagne, Nathan Lyon, Steve Smith, Mitchell Starc, Jake Weatherald, Beau Webster
Australia's World Test Championship fixtures:
3-0 away to West Indies, June-July 2025
4-1 at home to England, Nov 2025-Jan 2026
2 Tests at home to Bangladesh, Aug 2026
3 Tests away to South Africa, Oct 2026
4 Tests at home to New Zealand, Dec 2026-Jan 2027
5 Tests away to India, Jan-Mar 2027
Final: June 2027, Lord's