Giggs has been on leave from his post since November. He faces charges of assaulting two women and controlling or coercive behaviour – charges that he denies – and is due to stand trial in January 2022.
Page has shone in Giggs' absence, and the former Wales captain guided the Dragons to the knockout phase from a tough group that also featured Italy, Switzerland and Turkey.
Wales also had to deal with more logistical problems than most at Euro 2020 by having to play their opening two games 3,000 miles from home in the sweltering heat of Baku.
Switzerland outplayed them in the opening game, but character, determination and a Kieffer Moore header earned Wales a 1-1 draw and a precious point.
A 2-0 victory over Turkey – comfortably Wales' most accomplished display of the tournament – effectively sealed a round-of-16 place. Goals from Aaron Ramsey and Connor Roberts underpinned a performance that bristled with authority, pace and precision and had Wales fans dreaming again.
Wales could even afford for captain Gareth Bale to miss a penalty, but confidence levels were suitably topped up as they left Baku for Rome, where Italy awaited them.
The Azzurri triumphed 1-0, progressing as group winners, but it was enough for Wales to finish as runners-up and head to Amsterdam for a clash against Denmark in pursuit of a quarter-final spot.
Dutch coronavirus restrictions meant most Wales fans were banned from the game – unlike their Danish rivals – and, after a bright start, it eventually proved a game too far.
As Wales headed home, the tournament's third-youngest squad achieved a satisfactory mark from most fans and pundits and attention will now quickly return to a resumption of their 2022 World Cup qualifying campaign.
There are a number of questions to be answered, most notably how long Bale – who turns 32 next week – intends continuing his international career.
The Real Madrid star walked out of a television interview immediately following the Denmark defeat when asked about his future, although he subsequently said that he would never quit Wales while still playing.
With the World Cup in Qatar little more than 16 months away, Bale is expected to give it one more shot to grace football's biggest stage.
So, too, Wales' other thirty-somethings – Ramsey, Joe Allen, Chris Gunter and Wayne Hennessey.
With Page set to remain at the helm and the likes of Daniel James and Joe Rodon having enhanced their reputations at Euro 2020, there is no doubt that Wales have sufficient quality to book a first World Cup finals appearance for 64 years.
Belgium, the world's number one ranked one team, are the favourites to win the group and take the automatic place for Qatar 2022 on offer.
Wales lost their opening game in Belgium but bounced back to beat the Czech Republic 1-0 in Cardiff and boost qualification hopes before a September double-header away to Belarus and at home to Estonia.
Second place would secure a play-off spot, but Wales are almost certainly guaranteed that anyway due to their impressive Nations League performances last year.
Down, Wales most certainly were after losing to Denmark, but they are far from out after reaffirming their place among world football's leading nations.