It wasn't the first. With three to his name this season, the most recent of which saw him glance a clever header into the path of Aaron Ramsey for Arsenal's final goal in a 3-1 win over Olympiacos in the Champions League, Giroud is currently Arsenal's creator-in-chief, teeing up team-mates with more regularity than even Santi Cazorla or Mikel Arteta.
This statistic, though early in the season, speaks to the ability Giroud has to unsettle defences and the presence he brings to an Arsenal frontline that has lacked a muscular target man of his type for a number of years. Yet as the man who scored a league-high 21 times for Montpellier last season well knows, goals are the only measure by which practitioners of his particular trade are evaluated.
Giroud has one in Arsenal colours of course - a delicate chipped finish in the 6-1 hammering of Coventry in the League Cup - yet the France international discusses the matter as though he is searching for that elusive first goal after eight games, quite understandably given Arsenal's reluctance to treat the cup competition as a senior endeavour.
What likely weighs more heavily on his mind are the glaring misses - against Sunderland on the opening day, away at Liverpool and, at the weekend, when he spurned the chance to claim a late equaliser in what transpired to be a rather deflating defeat to Chelsea. The unflattering phrase 'the new Chamakh' has been sniggered in some quarters, but Giroud claims to be unaffected by any pressure, even if he does feel it. Discussing the start to his Arsenal career, he makes an effort to transmit confidence, even citing, unprompted, the fact that "Thierry Henry only scored in his ninth game for Arsenal, so it is a good example for a striker."
Inviting comparisons with the club's all-time record goalscorer, a man who accumulated 228 goals for Arsenal, is not the mark of a striker bereft of belief, and Giroud is certainly possessed of the expectation that he will soon leave his mark on the Premier League or Champions League, and extinguish the doubts that have been expressed about his ability.
"People say to me ‘the goal is coming soon, don’t worry, we trust you’," he says. "It is very important for me to feel the support of people and my team-mates too, so I think we are good.
"We lost against Chelsea but I think it’s an accident and we are confident for the future. Me too, I am confident and I want to keep going. Don’t worry about the future, the goals are coming soon. It’s like when you score one, you take confidence and more trust, you know. So, it’s like that when you’re a striker. You need to score but I’m not worried about that.
"He (Arsene Wenger) says sometimes I feel the pressure a little bit but I’m not worried about the pressure. I want to play and take a lot of pleasure on the pitch and we won (against Olympiacos) so it’s okay. Like you say, when I score my first goal in the Premier League, although I scored in the cup, it will be better and better."
Wednesday's win over Olympiacos brought further frustration for Giroud. Introduced as an 80th-minute substitute for Gervinho - who has conjured five goals in five games since unexpectedly being deployed as a rather unconventional centre-forward - he turned one cross from Theo Walcott into the belly of goalkeeper Balazs Megyeri before then seeing a firm effort smack into Dimitrios Siovas to prevent it nestling in the roof of the net.
Scrutiny from an expectant public and media continues as a result; talk of a drought swirling round him every time he enters the pitch. But after a bright cameo in the Champions League, Giroud hopes fortune turns decisively in his favour.
"I tried," he says of his 10 minutes against Olympiacos. "I try all I can but sometimes you need to keep the faith and keep going. Sometimes when you are a striker it is difficult. I don’t know why, but I try to do the right things. I think I am a little unlucky and sometimes I need to score. I don’t score but I am okay and I keep going. I continue to work hard in training and keep the trust.
"We won and the boss trusts me, my team-mates too, our fans too, and I want to continue. I feel good in this team. It’s okay, I continue to work harder and to score and to give a lot of pleasure to our fans."
Though Giroud openly admits "it’s quite difficult to adapt to the Premier League", he is enjoying being the latest in an ever-lengthening line of French ex-pats to find a home in North London. Former Tours team-mate Laurent Koscielny has aided the process, and Giroud says: "I feel very, very good in this city, with my team-mates and the people who work in this club, a very big club. I want to grow up here and keep going."
Settled off the pitch, he is still looking for his place on it. The process of becoming Arsenal's new centre-forward is as yet incomplete. As Giroud points out again before he departs: "I assist too, but I need to score."