British Racing Drivers' Club president Hill believes beyond that point the critics will soon start to question the 21-year-old.
Hamilton is now just a little more than two months away from his grand prix debut with McLaren, after being signed to partner two-time reigning world champion Fernando Alonso.
Hill feels if Hamilton can keep pace with Alonso, then his career should blossom.
"The first season is the toughest," said Hill, at the opening of the Autosport International Show in Birmingham.
"But all he has to do is be right on the heels of Fernando Alonso, two times world champion, and I think his confidence will grow and grow.
"You've a season's grace - maybe even half-a-season - because people will give him the leeway and the benefit of the doubt for that first six months.
"But then, at the end of the season, if he hasn't outpaced Fernando at one point or another, people will be saying 'Where is it? Where's that spark? Where's that thing?'
"Because you have to accept those that have gone on to become great drivers - like Michael Schumacher, Alain Prost, Ayrton Senna - they arrived and they went 'bang'.
"They were on the scene, on the pace, outpacing their team-mate - and they were there right from the word go.
"So it is fair to say there is a little pressure, but I don't think Lewis Hamilton is the sort of person who under-estimates that.
"I think he understands that and respects that. He's got a window of opportunity to learn, but it's going to be a short one."
Hill also issued a stern rebuke to David Coulthard, who has been one of the few to criticise McLaren for handing Hamilton a race seat.
Hill feels Coulthard's comments were borne out of the fact he is now at the tail-end of his Formula One career at the age of 35.
"David perhaps is revealing his slight reflection on the fact that he was a young driver once, like Lewis is," added Hill.
"Lewis is the future. He's going to be in F1 for a good few years, and let's hope that Lewis has more success and makes more of his opportunities.
"You have to say it's now possible to reflect on DC's career in that respect. I think it's not well founded, that assessment.
"I think Lewis has a proven track record of being a winner in GP2, and he's been well coached and guided by a very professional team in McLaren and Ron Dennis."
Hill also suggested Coulthard's opportunity to become a world champion had passed him by, even though he himself did not win the title until he was 36.
Coulthard, who now drives for Red Bull Racing, has been defended by team boss Christian Horner who claims he has never seen the Scot more committed.
"He has worked extremely hard in the past two years with the team," said Horner.
"He has been an instrumental part with the team and he has gone about his off-season with more effort than before.
"He is training harder and he is physically fitter than he has ever been.
"He is motivated, anxious to get going and looking forward to seeing how the new car goes.
"He has big expectations for the season ahead, and I have not seen him more motivated or fitter."
The stig