Overnight Conway wrote himself a place in New Zealand cricket history, scoring a century on debut and at Lords, the home of cricket.
Not only that, Conway has set a record for the highest score on test debut at the ground, passing former India batsman Sourav Ganguly's score of 131 in 1996.
The South African-born batsman reached 136 not out at stumps, guiding New Zealand to 246 for three after Williamson won the toss and chose to bat first.
He told RNZ's Morning Report today it was a dream start to his test cricket career. He has had to wait to become eligible to play tests for New Zealand, though he played three ODI's and 14 T20 internationals over summer.
And he revealed how he was in awe of the names of the cricket legends who have scored test centuries listed on the famouse Lords honours board.
"When we first got to the ground we had the opportunity to look at all the legends and names of the greats up on that honours board," he told Radio New Zealand after his innings.
"And I asked Kane how he felt seeing his name up on that honours board. I asked what is it like to see your name up on the honours board.
"When I got back in after batting, the first thing he said to me was 'now you know how it feels, bro'."
Conway shared in an unbroken 132-run partnership with Henry Nicholls, who's unbeaten on 46, and he says he could hear Nicholls cheering him on as he hit a boundary to bring up his century.
"It was a great feeling. As the ball was heading to the boundary, I just knew it was in the gap. And I couold hear Henry Nichols, saying 'yes boy, yes boy'."
Conway has had to wait for his test debut - he is a few weeks short of his 30th birthday. And overnight he had to wait for his first ball in test cricket - perhaps it helped.
"I had to wait three or four voers to face my first ball, but I was pretty grateful. I got to watch from the non-strikers end. I got used to what the ball was doing off the surface and I got to have talks with Tom Latham about how it was playing."
At times, he did face a barrage of shorter pitched bowling from England's Mark Wood in particular.
"I thought at the length he was pitching, the ball should go over my head but on this surface it skidded through. After I had worn a few on the body, I thought it was time for Plan b; let's change this."
And he did. Conway showed very few nerves or chances as he worked his way to a century and beyond.
"Just getting a test debut and the chance to play at this level was not something I'd thought about. Very special feeling."
New Zealand won the toss and chose to bat but they lost opener Tom Latham in the first session while skipper Kane Williamson and Ross Taylor fell cheaply after lunch even as Conway took control.
Conway has set a record for the highest score on test debut at the ground, passing former India batsman Sourav Ganguly's score of 131 in 1996.
"The job's not done but I'm very happy.
"Just getting a test debut and the chance to play at this level was not something I'd thought about. Very special feeling."
Conway and Henry Nicholls (46 not out) stitched together a patient 132-run partnership to steady the ship and set up a platform for their deep batting lineup on day two.
England went with four fast bowlers on a green wicket but, barring a few unsettling deliveries, Conway saw off the early threat from James Anderson, Stuart Broad, Mark Wood and Ollie Robinson before slowly growing into the game.
England debutant Robinson drew first blood to dismiss Latham for 23 after the opening batsman had an inside edge crash into the stumps.
Anderson, playing his 161st test match to equal former captain Alastair Cook's record for most England caps, then got rid of Williamson in the first over after lunch - the seventh time he had dismissed him in tests.
Williamson looked to defend a rising delivery but the ball spun back to hit the top of off stump and he walked back to the pavilion for 13.
Taylor (14) followed him soon after when a Robinson delivery sneaked past his bat to rap him on the pads as England successfully appealed for leg before wicket.
England bowled better in the second session to keep the run rate down but struggled for variety without a specialist spinner in the side, forcing captain Joe Root to try his luck with 12 overs which did not yield a breakthrough.
Lord's welcomed back spectators for the first time in nearly two years but limited capacity to 25% due to the Covid-19 pandemic.
- additional reporting by Reuters
