Debuting so close to "Crisis on Infinite Earths" was never going to be easy for The CW's Batwoman. Trying to establish new characters, introducing a new version of the Batman mythology, and setting up a new series is already a tall order for anyone. Along with the build-up to Crisis, it’s almost too much to do at once. So, to help ease the process, they introduced Batwoman as part of the 2018 crossover event, Elseworlds.
However, solving this problem just added another one: the show’s timeline now makes no sense. Having been part of Elseworlds and Crisis on Infinite Earths has added a glaring problem to the timeline of Batwoman. Rather than catching us up to the crossover, it’s just made things even more confusing overall.
In Episode 5 of Batwoman, we start getting more insight into the timeline. Luke tells Mary about the breakout at Arkham Asylum, directly referencing the events of "Elseworlds." It’s a good moment to catch the show up with what we’ve already seen, and by itself, it doesn't necessarily mess with the timeline. All we know before this is that Elseworlds is sometime after Episode 3 when Batwoman finally upgrades from the repurposed Batsuit to her first custom Batwoman costume. Thanks to Luke's comments, we get a more specific timeline.
Then "Crisis on Infinite Earths" happens, and the events of "Elseworlds" are referenced as having happened a year ago. While this may be the case for Barry and Oliver or even Kara, Batwoman hasn't been active long enough for that to be the case. Even with Luke referencing the breakout in the past tense, that only gives it a couple of weeks. These shows also have a tendency to move forward about a week an episode, leaving about a 10-month gap unaccounted for.
We can tell the gap is there because of the immediacy of Batwoman's ongoing narrative. Alice seems to have been escalating her attacks on the city, not waiting around for months. Crisis also has Kate telling Kara about Catherine’s death, making it sound like a pretty fresh trauma. This would fit the roughly one week an episode cadence of the shows, but that would still put it a few months prior to Crisis at best.
Maybe Batwoman just hasn’t caught up yet with the other shows, time-wise. This might be a little clunky as an explanation, but it doesn’t have to be perfectly linear. If you fudge the timelines a bit and make a specific reference later in the season, like looking up to see the red skies, you can make it work. We’ve already seen this way of handling a crossover before in the Arrowverse, with The Flash handling its first crossover with Supergirl like this - Barry only makes an off-hand reference a few episodes later, never even directly namedropping where he was or who he met. As of now, we’ve seen no specific reference to the red skies in Batwoman, so it could be that Kate sees them later in her own series.
Of course, Batwoman could just ignore the minutia as well. Some previous smaller crossovers glossed right over the details. When Oliver helped Barry defeat the Reverse Flash in season 1 of The Flash, it never was explained how he managed to get away from the League of Assassins long enough to help Barry in Central City. Fans were confused, but gave it a pass because it was a good moment. It's entirely possible that Batwoman just never directly references when "Crisis on Infinite Earths" takes place in favor of keeping with its own pacing.
And there are of course the far-fetched magical solutions. In "Elseworlds," Batwoman only appeared when the world was under the influence of the Book of Destiny, not in the “real” world. We know Oliver and Barry switched bodies in Elseworlds, but what else was different? Making that Batwoman merely a product of the Book of Destiny may feel like a cop-out, but the Book has unclear enough powers that writers could make it work.
Ultimately, the timeline is only a concern for fans who want the math of the timeline to line up consistently. For now, though, what's important is that Batwoman is proving to be another hit for The CW and with fans, with ratings that rival The Flash. Whether or not the timeline gets fixed may not actually matter, as long as the show just keeps being good.