Mateo, born prematurely in December 2017, spent the first five months of his life in hospital.
Silva, returning to the side after injury to make his 250th Premier League appearance and with his baby son Mateo at the game, was inspired.
Sergio Aguero netted the first hat-trick of the new top-flight campaign, while Gabriel Jesus, David Silva and an own goal from Terence Kongolo also contributed to a heavy defeat for the visitors. He scored an unbelievable goal for him.
Guardiola confirmed yesterday that De Bruyne would be out until the middle of November because of the lateral collateral ligament injury he sustained during a simple training exercise on Wednesday.
When David Silva's son Mateo was born late previous year, the Manchester City midfielder took time away from football.
Guardiola shuffled his starting lineup and started with a back three, Bernardo Silva and Mendy as wing-backs and a front two of Aguero and Jesus.
"I have to say Liverpool look outstanding", Sinclair told Yahoo Sport Presents The Football Show on Friday. Since he came back and I saw him from the first minute, I said: 'Wow!' It's part of the game, part of the amount of games and seasons, games and seasons (they play) and in the end the players fall down.
Last season's success was built on two morale-boosting opening victories albeit the opposition was entirely different - Crystal Palace during Frank de Boer's disastrous brief spell in charge and fellow promoted side Newcastle United.
City's rampant display underlined why they are such strong favourites to retain their title. The Australian is one of the few players capable of making a pass under pressure and his composure was missed in the centre of the pitch.
City were already beginning to think about how many goals they could score against opponents who were offering nothing in the final third but just before the break, a long throw was flicked on by Mounie and Stankovic was able to reduce the deficit with a confident finish from close range.