Manchester City will take Liverpool into account regardless of the first few games. I believe that at Manchester City there is a level of professionalism that doesn't allow for any of their competitors to be underestimated for as long as it is mathematically possible to be overtaken by them.
That's how Guardiola does his job all the time. Never give a few percent less than you can until the deal is finished. It can be seen when he complains after any of their wins. I hardly saw him saying that he is 100% satisfied with the performance.
The way Pep Guardiola handles his team is different from how other managers does. He hardly gives credit to his players even when they win a match. He knows they are not 100% perfect but he always make them feel that they can do more and the ones they already performed is not enough to call them satisfactory. This has given them a competitive edge against their competitors which always works for them almost all of the time. Manchester City don’t consider a team as being a big team or small team, they always give in their best and make sure they win a team with lots of goals and this always give them an edge in terms of goal difference even when they are been caught up by their close competitors.