Chief executive Scot Gardiner says Dundee are ready for "a great adventure" as they make their top-flight return after seven years away.
Dundee were late replacements after Rangers headed for liquidation.
We would have liked a few more weeks' notice, but we are where we are," Gardiner told BBC Scotland.
"If we bring in the right players, by the end of August, I think you'll see a good Dundee team ready to make a right go of it."
Manager Barry Smith had already signed three new players and made Carl Finnigan's loan from St Johnstone permanent in preparation for another assault on promotion.
But they waited until confirmation of a new Scottish Premier League television deal before
adding former Brussels defender Davide Grassi and released Bradford City striker Mark Stewart.
"We had a First Division budget and we were working to a First Division budget until two weeks past Monday.
"Then we got the decision we were hoping for, but it's been absolutely manic and meetings until late in the night with agents pretty much from all over Europe.
"Barry feels that we certainly need six. We'll bring in six and that might not be right up until the end of the window.
Declan Gallagher was signed from Clyde in preparation for Division One
"We can't make many mistakes, so we've got to make sure they are the right boys that come in."
Gardiner said bringing the club up to SPL standard behind the scenes will eat into any extra income they will receive.
"We need to manage it very carefully and not put the club at risk," he said.
"This should be a chance for us to build a bedrock and platform for the club going forward."
Gardiner thinks Dundee's return to the SPL, and their rivalry with neighbours United, will be "phenomenal" for the city.
He predicted that up to 3,000 Dundee fans would travel to Kilmarnock for their opening fixture.
Gardiner thought that Celtic would be strong favourites for the title but pointed out that other clubs had been unable to strengthen significantly because of a lack of finance.
"There's a little mix of trepidation, because we had built a good squad and were planning to win the First Division, and a tremendous amount of excitement," he said.
Dundee have already played one competitive fixture, with Smith having to name himself as a substitute for his injury-hit squad as they struggled to overcome Third Division Peterhead on penalties after a 0-0 draw in the Scottish Communities League Cup.
The manager said his side also had to learn from their derby defeat in a pre-season friendly, when more than 10,000 fans watched United win 3-0.
"I think the massive difference was how clinical United were," he said.
"But, in general terms, I think we competed well for 70 minutes, but the wee lapses in concentration are what we'll need to work on.
"We have to work harder than we ever have before to make sure we remain in the Premier League.
"It is a great opportunity for myself and the players to go and do well in the Premier League.
"We've not had a lot of time to strengthen the squad, but I'm sure, come Saturday, everybody will be ready to play their part in getting off to a good start."