Kay will pack down with Ireland's Paul O'Connell against Bay of Plenty in Rotorua, the first of six tour matches the Lions have scheduled leading into the first Test on June 25.
But Woodward will realistically need to have decided the majority of his Test side by the fourth run-out, against Wellington on June 15.
Time is short but Kay, a member of England's World Cup-winning side, is relishing the pressure.
"We are not going to get a lot of opportunities so when they come along in the starting XV you have to make the most of it," said Kay.
"That pressure is a good thing and it should increase the performances of the guys that are all desperate to get in the squad for the Test matches.
"When it comes round to the Tests you only have one opportunity to win the series so that pressure is probably a good grounding for the team."
Bay of Plenty will be no pushovers. They relieved Auckland of the Ranfurly Shield - a significant achievement in New Zealand rugby - and finished third in the National Provincial Competition.
The Lions have been studying what footage they have been able to cobble together and expect Bay of Plenty - also known as the Western Bay Finance Steamers - to compete heavily at the set-piece.
In short, there is unlikely to be a repeat of the Lions tour opener four years ago, when they racked up a century of points against Western Australia in a match which did little to prepare them for the battles to come.
The Lions want a tough test. It will allow the players to prove themselves in a competitive environment and give them a steel ahead of the Test series with New Zealand.
"The All Blacks seem to have got stronger since Graham Henry took over, particularly in the tight phases of the game," said Kay.
"It's going to be a combative All Blacks team we face and they are very skilful but they have that killer edge. There will be a bit of bite about them."
Kay does not subscribe to the general view that the All Blacks could be vulnerable in the tight five when the Test matches come around.
"If that's a weakness I wouldn't like to see a team at full strength. Whenever I have played in New Zealand it has been a good battle up front. (Lock) Chris Jack is an awesome player and whoever plays with him is going to give us a tough time," he said.
"But lock is one of the strengths in the British & Irish Lions team. There are a lot of good players. It is going to be tough for all of us to break into the Test team."