Mr Givan said his party needed to see draft legislation to scrap the bulk of the Northern Ireland Protocol taken through Parliament before it could countenance a return to a devolved executive.
The DUP has faced calls to start re-engaging with Stormont, even to allow the nomination of a speaker, before the Assembly’s summer recess.
But Mr Givan said dates on a calendar would not influence his party’s stance.
He was speaking after Stormont’s main parties met to begin discussions about what a potential programme for government might look like when and if powersharing returns.
At the meeting the head of the civil service, Dr Jayne Brady, outlined some of the challenges facing public services in Northern Ireland in the continuing absence of a functioning administration.
Last week the Government tabled a Bill at Westminster that would empower ministers to override much of the contentious post-Brexit trading regime it agreed with the EU in the withdrawal talks.
The DUP has blocked the establishment of a new ministerial executive following last month’s Assembly election in protest at the protocol, which has created economic barriers between Northern Ireland and the rest of the UK.
The party has made clear that tabling the legislation is not enough to convince it to return to the executive, saying it needs to see tangible delivery on removing the so-called Irish Sea border.
Mr Givan said the protocol was the “elephant in the room” during Monday’s meeting at Stormont Castle.
“There’s good engagement across the four parties that can form an executive and obviously the elephant in the room in all of this is trying to deal with the protocol, and we need to see that legislation taken through Westminster, remove the Irish sea border, the barrier that’s creating this executive from being able to form, and then we can make progress and hit the ground running and deliver for the issues that matter to people,” he said.
“It’s the conditions that we’re looking for, not a calendar, and when those conditions are met Jeffrey Donaldson (DUP leader) has made clear that there will be a graduated response from the party, and it’s for the Government to move that forward and expedite that as soon as possible.
“We’re ready, we now need to see that delivery from the Government.”
Dr Brady has initiated a process whereby the party leaders will meet every two weeks to discuss planning for a future executive. The parties will also nominate MLAs to sit on working groups that will focus on some of the key priority areas.
Sinn Fein vice president Michelle O’Neill, who would be in line to become the party’s first first minister if an executive was restored, said the DUP’s block on powersharing was “unfathomable” given the pressures facing families in the region.
“We’ve met this afternoon with the head of the civil service and she certainly painted a very bleak picture in terms of the difficulties that lie ahead,” she said.
“The reality is that the DUP’s blockage of the Executive is preventing us from being able to agree a budget and is preventing departments the ability to be able to plan for what is going to be a very, very difficult period ahead, certainly the winter months are going to be probably the most challenging the people have ever seen in terms of the cost-of-living crisis.”
She added: “Particularly when we hear today just how difficult it is going to be in the autumn and winter for people, it’s just unfathomable that we don’t have an executive in which to respond to that.”
Alliance leader Naomi Long said the Government should cut the pay of DUP MLAs if they continued to block the return of Stormont.
“It’s fairly clear to me that it’s a dire situation that we’re in,” she said.
“There is money there that we can use, it’s not enough, of course it’s not enough, but it would be better than nothing, and yet it sits in the centre and we can do nothing useful with it.
“And I think that’s scandalous at a time when people are really struggling.”