With players fresh off an unexpected break following last week's two-day debacle in Melbourne, Albanese and his wife Jodie Haydon hosted both sides at Kirribilli House on Thursday night.
Their dog Toto briefly appeared and greeted both teams.
Usman Khawaja began a game of cricket with his children and several others on the lawn, while at one stage a ball was hit through a fence and towards the harbour.
Addressing both sides, Albanese remarked that the SCG would "hopefully" go for five days, before urging the teams to ensure it was not another two-day encounter.
Day three is the main day for the McGrath Foundation, with over $8.5 million raised for cancer support nurses across last year's Test.
"Day three in this Test is really important," Albanese said.
"More so than the others.
"So whatever you do, if things are going wrong, just get someone to play out a couple of sessions, because we do want day three.
"It's something very special with the virtual seats that are sold and everyone participates there as well."
The McGrath Foundation has endured some bad luck in the past, with the day three Jane McGrath Day completely washed out three years ago against South Africa.
Albanese's comments come after players were greeted with an extremely green SCG wicket when they arrived for training earlier on Thursday.
Venues NSW chairman David Gallop was spotted on the ground talking to chief curator Adam Lewis, and grass coverage is expected to be reduced before Sunday.
This summer's Tests have been the shortest in Australia since the 19th century, with an average of 232 overs per match.
Melbourne and Perth have ended inside two days, costing Cricket Australia around $15 million in revenue and an estimated 210,000 people through the gates.
Taking to the microphone in response to thank Albanese for hosting his side, England captain Ben Stokes joked his speech would "probably go like Perth and Melbourne" in length.
"The cricket hasn't gone as we would have liked it to, but Australia holds some special memories," Stokes said.
"We came here with a goal in mind, we didn't quite manage to achieve it but we get to play in some pretty iconic Test matches."