The Finn arrived at the Amex Stadium with experience of the Champions League as both a player and a manager, but so far has struggled in the second tier of English football.
However, he will be hoping to kick on now that his side have finally got their first league win of the season under their belts, beating Leeds United 2-0 at Elland Road on Tuesday.
That match saw the Seagulls not only pick up their first win and points of the season, but also saw them score their first goal of the league campaign, with Joao Carlos and Kazenga LuaLua both finding the back of the net.
The result will be a big weight off the broad shoulders of Hyypia, who had seen his playoff contenders fall to disappointing defeats at the hands of Sheffield Wednesday and Birmingham City in the first two matches.
The former Liverpool defender has a big task on his hands to replicate the success of the past two seasons, however, having lost eight players that started the first leg of last term's playoff semi-final.
Whereas Brighton ended their search for a first victory of the new league season in midweek, Bolton Wanderers are still looking for their opening win of the campaign.
Dougie Freedman's side have made a disappointing start in the Championship, losing heavily to Watford on the opening day before a draw and a loss against Nottingham Forest and Middlesbrough respectively.
As a result, they sit in the relegation zone at this early stage of the season, and Freedman will be desperate to escape the bottom three as soon as possible.
If they are to do that this weekend, then they could do with loanee Joe Mason once again finding the back of the net having scored just four minutes into his return to the club last Saturday.
Craig Davies is likely to be another key player, having won and scored a penalty against Middlesbrough, but Freedman also needs his defence to be able to hold on to these leads.
Possible starting lineups
Brighton: Stockdale; Calderon, Greer, Dunk, Chicksen; Bruno, Agustien, Holla, Carlos; Forster-Caskey, Mackail-Smith
Bolton: Bogdan; McNaughton, Mills, Wheater, Ream; Feeney, Spearing, Trotter, Lee; Mason, Davies
Sports Mole says: 1-2