New Zealand-born White, 33, looked set to earn his first Ireland cap last autumn only to suffer a broken arm.
However, coach Joe Schmidt kept the door open to the Connacht prop even when he suffered a further back injury.
"I don't know how many coaches would show that kind of faith," said White.
"When I injured my arm back in November that was very disappointing, but then to get fit and injure my back, there were definitely a few demons.
"But Joe's backed me and given me a crack, and it's just fantastic to have had that chance.
"There were dark days in rehab but the carrot was always to be in the position to play in a game like this, so it's great to have done it.
"Connacht offered me a new contract though, so that really made me determined to get myself right and do right by them."
Leinster stalwart Mike Ross remains the only player to feature in every Test in the Joe Schmidt era and has the starting tight-head spot nailed down for next month's World Cup.
Marty Moore will provide the immediate back-up if he recovers from shoulder trouble in time as expected, leaving White battling it out with Michael Bent for the last prop berth in Ireland's 21-man World Cup line-up.
Bent's ability to prop on both sides of the scrum offers versatility but White's unfussy solidity may yet see him trump his main rival.
White himself was simply happy to have made his long-overdue Test debut as Ireland edged out the Scots 28-22.
"I felt like a kid again myself, especially when you've got Paul O'Connell out there, a guy I've watched for a fair while.
"So I just really wanted to cherish the moment.
"If Joe's happy with what I've done on the field then hopefully I'll get the call to go back into camp on Sunday night."
Nathan White was thrilled to make an Ireland debut that he feared was destined never to happen as he came on in the second half of Saturday's World Cup warm-up win over Scotland.