Wilshere was left on the bench by England Under-21 coach Stuart Pearce for the recent European Championship qualifying win over Portugal, amid concerns the player's focus was not right following his arrest and subsequent bail after a late-night fracas in Kensington.
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Wilshere, who set a new record as the youngest Arsenal first-team player in the league and Europe during September 2008, declared: ''It is good to get games and hopefully I can push on from here.
''I am just trying to break into the Arsenal first team.
''Last year, I had to go out on loan to get some games because there were some world-class players at Arsenal, but I have come back with more experience and the boss thinks I am ready to challenge for a place.
''All I can do is challenge and show them what I can do.''
Wilshere continued: ''It is perfect playing with Cesc and Alex Song in midfield.
''Playing with people like Cesc Fabregas makes it easy for you.He will talk to you and talk you through games.
''You saw what Cesc could do against Braga - it is perfect for me to learn from him.''
The comprehensive victory over the Champions League newcomers continued Arsenal's impressive start to the new season - netting 12 goals in their three home games.
While Wenger maintains none of his squad will get carried away on their early promise, Wilshere sees no reason why the young Gunners cannot stay on course to deliver success.
''This year we are ready to go on,'' he said.
''It gives us an incentive with the final at Wembley.
''Hopefully we qualify from the group and then we see what happens.''
Wilshere was a constant menace in and around the Braga penalty area last night, while also helping break up play in midfield.
Indeed, but for a fine save from busy keeper Felipe, he could have got on the scoresheet himself.
Wenger believes the 18-year-old has matured a lot in the past 12 months.
''The loan spell was important because it accelerated his career by being confronted in the Premier League and having tough games,'' the Arsenal manager reflected.
''Jack has been educated here and he was already an outstanding player when he left for Bolton, but this is the final part of the education of a player - to be integrated into the first team and play under pressure. That was important for him.''
Wenger, though, admits he did not expect Wilshere, who has three Premier League starts already, to feature so prominently at this early stage of the campaign.
''Football teaches you one thing - be open-minded and never have a definite opinion,'' he said.
''You need to have opinions sometimes, but you always have to have an open mind on players because you can never predict how quickly they develop.''
Midfielder Abou Diaby is set for a spell on the sidelines, having been ruled out by an X-rated tackle from Bolton's Paul Robinson, which went unpunished by referee Stuart Attwell, but centre-half Thomas Vermaelen could return at Sunderland on Saturday following his Achilles problem.
Arsenal will face another test of character at the Stadium of Light, where they went down 1-0 last November just after the international break.
Defender Gael Clichy maintains this time, the Gunners must show their true championship credentials.
''We know how difficult the Premier League is so we have to recover quick because we know Saturday will be a battle,'' he said.
''They are good at home and we just want to show that we can perform week in week out.''