All things created equal, Ant Man and the Wasp should pick up 2 years after Civil War, but shortly before Infinity War. Ant Man wasn't called during Infinity War because he was still under house arrest. Infinity War seems to take place over only a few days.
Given this, and in relation to Infinity War, when exactly does the end (end of the movie, not the mid-credits scene) of Ant Man and the Wasp happen?
A little more than two years after the end of Captain America: Civil War, and prior to the snap in Avengers: Infinity War.
At the end of the movie, Scott Lang has just finished serving his two-year sentence under house arrest, meaning that the movie's end occurred a little (to allow for sentencing, etc.) over two years after the end of Captain America: Civil War. It also must have occurred prior to the snap in Avengers: Infinity War, as the results of the snap are portrayed later in the mid-credits sequence.
Your real question, though, is why Scott Lang was never called in during the events of Avengers: Infinity War, since according to this timeline he should already have been free by the point when Cap's faction reunites with Rhodey and Banner. But this is Romanoff's actual line:
After the whole Accords situation, he and Scott took a deal. It's too tough on their families. (Avengers: Infinity War)
In other words, they never explicitly say that they aren't calling Barton and Lang in because they're under house arrest, merely that they aren't calling them in because they "took a deal." Even though Scott Lang was no longer under house arrest by this point, he's still under probation and was presumably not in contact with either Cap's faction (who were still fugitives) or the official, Accords-sanctioned Avengers (whom he had no ties with to begin with).
Given this, and in relation to Infinity War, when exactly does the end (end of the movie, not the mid credits scene) of Ant Man and the Wasp happen?
I'd venture a guess it was approximately 2 years and change after the events of Civil War. Scott Lang had just finished his two year house arrest sentence, so it'd have to be at least two years, in addition to how ever long it took for his court appearances and sentencing.
His sentence, for his actions in Germany in Civil War, was two years house arrest, which ends just as the film ends, followed by three years of probation. Assuming the trial and sentencing after Germany was fairly swift, that would set the end of the film as "a little" (two - three months, max, is my guess) more than two years after Civil War.
The whole of the main film takes place before Infinity War. The period of time between the end of the film and the mid-credits sequence is unspecified - a few weeks may be a fair guess. It's only that sequence that syncs exactly to the climax of IW. So that would set the end of the film at "a little" before the events of IW. The events of IW took place so quickly, it's possible he simply missed any news reports of the fighting, or perhaps he just figured since he couldn't (legally) help, it wasn't his business, so he spent no time thinking about it.
During Infinity War, someone asks where Scott and Clint are, and their plea bargains and house arrests are mentioned. Based on this timeline, Scott would have been been released from the house arrest, but still just starting his three year probation period, so he still wouldn't have been able to help without legal repercussions. They may have not recalled the exact length of the sentence, or they just simplified the line to avoid slowing the moment down.
