Elsewhere, Cristian Volpato scored a terrific goal for Serie A club Sassuolo, Mohamed Toure claimed a double for English Championship side Norwich, and Lucas Herrington enjoyed a second Premier League win with Hull.
Goalkeepers Patrick Beach and Maty Ryan continued their fine form with Troyes and Levante respectively.
Okon-Engstler, son of former Socceroos captain and current assistant coach Paul Okon, joined FC Köln from Sydney FC after an impressive World Cup, where he impressed as a creative holding midfielder.
The 21-year-old started and played 65 minutes as Köln defeated Hoffenheim 3-2 in their season opener.
Volpato has two goals across all competitions already this season and notched his first in the Serie A campaign.
The exciting attacker curled a terrific first-time left-footed strike home to kick off Sassuolo's 2-1 win over Torino.
Herrington, 18, came off the bench to help Hull keep a clean sheet and seal a 1-0 win over Coventry City.
Toure had a difficult World Cup, scarcely used by coach Tony Popovic, but has picked up where he left off at English championship club Norwich, netting two clinical finishes in a 4-1 win over Burnley.
The South Australian striker has 13 goals in 16 appearances across all competitions since joining the Canaries at the start of 2026.
Beach made four saves in a man-of-the-match performance for Troyes, who claimed a 2-1 win over Lorient in France's Ligue 1.
Ryan was in goal as Levante beat Real Betis 5-2 in Spain's LaLiga.
Right-back Jacob Italiano returned from injury off the bench in Grazer AK's 0-0 draw with Wolfsberger in the Austrian Bundesliga, marking his first game since he had to depart Australia's World Cup squad early.
Riley McGree, who missed the World Cup through injury, started and played 69 minutes as Middlesbrough beat West Bromwich Albion 3-1 in England's Championship.
Nestory Irankunda played nine minutes off the bench as second-placed Sporting CP beat Rio Ave FC 4-0 in Liga Portugal.
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