"I think the most important thing now is for us to look to the horizon, to raise our eyes to the horizon, think about the future, think about the new partnership - the deep and special partnership - that we want to build with our friends".
Davis and the EU's chief negotiator, Michel Barnier, meet with the United Kingdom keen to win back sovereignty without hurting its economy, while the EU's aim is to maintain regional stability and stop inadvertently rewarding Britain's decision to leave for fear of encouraging others to break away.
The formal negotiations kick off after British Prime Minister Theresa May's Conservative Party performed poorly in a recent snap election she called in order to provide her with more leverage during the Brexit negotiations.
Officials on both sides play down expectations for what can be achieved in one day.
Britain has already made concessions by agreeing to the European Union proposals to sequence the talks, by postponing trade discussions until broad agreement is reached on a cash "divorce settlement", the Northern Ireland border and the rights of European Union citizens in the UK. "A deal like no other in history", Davis said in a statement as he headed into the talks.
"Sitting down for a first formal negotiation round is something in and of itself", an European Union source told AFP. Only when there is "sufficient progress" does the European Union want to look at creating a new relationship with Britain on things like trade and migration. Yet Davis entered the talks representing a government in disarray.
In an interview with the BBC's Andrew Marr, the chancellor ruled out continued membership of both the European single market and the customs union.
A spokesman for the Department for Exiting the European said: "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account".
Anxious by immigration and loss of sovereignty, Britain voted past year to end its four-decades-old membership of the 28-country bloc - the first state ever to do so - in a shock referendum result. Some of her ministers want to refashion her strategy toward protecting trade with Britain's biggest market rather than continue to aim for her original goal of winning control of immigration and law-making.
With a further million British expatriates in the EU, Ms May too wants a deal on citizens' rights, though the two sides are some way apart.
Last year's Brexit vote came as a profound shock to Brussels against a backdrop of rising anti-EU sentiment, with many - including now US President Donald Trump - predicting the bloc's eventual break-up.
Brussels is also resisting British demands for immediate talks on a future free trade arrangement. The election of the fervently Europhile Macron, and his party's sweep of the French parliament on Sunday, has revived optimism in Brussels.