A slog it may be, forcing the Hammers to start their season more than a month before their domestic rivals, but supporters will not be complaining too much as their side embark on a first European campaign in nine years.
Many British teams fell at the first hurdle, with the likes of Glenavon, Glentoran, Broughton, Bala Town and St Johnstone each crashing out, leaving West Ham, Linfield, Newtown and Aberdeen to continue their journeys.
Here, Sports Mole looks at each second-round qualifying fixture in more depth, while also taking a look at those who join the draw at this stage.
West Ham United vs. Birkirkara FC
Until Tottenham Hotspur, Liverpool and Southampton enter the fray, all eyes will be firmly fixed on West Ham. The Hammers could afford to field a team mixed with experience and youth against Lusitanos in the first round, and that is likely to be the same case as they close in on the Europa League proper.
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Maltese opponents Birkirkara will require something close to a miracle to overcome the Premier League club, but they will be boosted heading into next week's fixture having just won their first ever European match away from home.
Club president Adrian Delia claimed after the 3-1 victory over Ulisses that his charges would be ready for the challenge of West Ham on the back of their "historic" win in Armenia. Four-time champions of the Maltese Premier League, the Stripes will very much be relying on home form against Slaven Bilic's side.
Birkirkara have won 15 of their last 23 matches at the Infetti Ground, losing just two of those fixtures to prove their ability. West Ham will offer a different threat altogether, though, which is likely to spell the end of the Maltese side's run in this competition for another season.
Rijeka vs. Aberdeen
If proof were needed of just how tough these early rounds of UEFA's secondary competition can be, then look no further than St Johnstone's defeat to Alashkert FC on Thursday night. Despite being a goal to the good and seeing their opponents reduced to 10 men, it was the visitors who bagged an all-important away goal to progress through.
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Next up for the Scottish outfit is a difficult-looking fixture against Rijeka, a club with plenty of experience in these early throes of the competition. In each of the last two campaigns, they have brushed aside all before them to reach the group stage.
Fellow British outfit Prestatyn Town had eight goals shipped past them without response in 2013, while it has been 12 outings in Europe since they last suffered defeat on home soil. That is no mean feat, either, considering that each of Real Betis, Lyon, Standard Liege, Feyenoord and eventual winners Sevilla have all played here over the past two years.
Joining Aberdeen in the second qualifying round will be Inverness, who bypass the first batch of fixtures following their Scottish Cup triumph last season. They will face off against a familiar foe of sorts, with Astra having competed against Scottish opposition Celtic in last season's group stages.
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Celtic set the benchmark by getting the better of the Romanian outfit over the two games, but they could only manage a draw at the Stadionul Marin Anastasovici in difficult weather conditions.
Astra did pick up victories over Lyon and Dinamo Zagreb, however, proving that they should certainly not be dismissed at this stage. The Black Devils, formerly known as Astra Ploiesti until 2012, only actually made it this far by default. Romanian club Universitatea Cluj filed for insolvency, while fellow finalists Steaua Bucharest were already guaranteed a place in Europe thanks to their strong league position.
That meant that Giurgiu, who only finished in fourth place, were handed a reprieve ahead of an FC Cluj side who were not handed a UEFA licence. In fact, 10 of the division's 18 side are not currently eligible to play European football.
Spartak Trnava vs. Linfield FC
They may hardly be a well-known name on British shores, but St Johnstone supporters will certainly warn Linfield not to underestimate Spartak Trnava. That is because the Slovak side dumped the Saints out of the competition in the final qualifying stage 11 months ago.
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Trnava managed to edge out Senica to finish fourth in the Slovak top flight last term, despite winning just one of their last five games. They may have managed to reach the semi-final of the European Cup once and the quarter-final twice, yet success has been hard to come by in more recent times.
The White Angles often fail to get beyond the qualifying rounds, tasting defeat to Zurich at the playoff stage last season to see their hopes dented once more. It is a similar tale for Linfield, though, who themselves struggle to make it into the competition proper.
A slender victory over NSI Runavik this week will of course give them hope, but if they are to navigate their way past Trnava, then they will have to be on top of their game across both legs.
Copenhagen vs. Newtown AFC
Wales' solo representatives face an almighty task if they are to take their European aspirations beyond the month of July, having been pitted against Danish giants Copenhagen.
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Newtown did brilliantly to overcome Valletta in their opening fixture, greeting the referee's full-time whistle in Malta with scenes of joy. The journey now continues with a trip to the Danish capital, where Stale Solbakken's charges await.
Copenhagen, who enter the competition at the second qualifying round due to their domestic cup exploits last term, will be looking to Cardiff City flop Andreas Cornelius to fire them through. The 22-year-old is aiming to return to his best form on home shores following a disappointing spell in English football, which is a similar case for boss Solbakken.
The Lions flopped in the Europa League last time out, however, losing four of their group games and winning just one. That may paint a picture of a side who are inept at this level, but their past record shows that is far from the truth. Newtown, it could be said, have been dealt the short straw as far as their European hopes are concerned.