TL;DR - It looks like it will take less than 2 hours of playtime per day to reach tier 55 by the end of the 2nd week, unlocking the latest hero by day 1 of them being available in competitive.
While not 100% confirmed, it looks like every tier in the OW2 battle pass will be 10,000 xp. It’s also not 100% confirmed, but let’s assume the experience gain/leveling rate is similar to that of Overwatch 1. Last assumption: It looks like there will be at least 11 weekly challenges, and they will net 5000 xp each. Let’s speculate there will be 3 dailies at 1,000 xp each.
If the above is true, we can say it takes 550,000 xp to reach the hero on tier 55 via F2P, which is equivalent to 25 levels in OW1. If you were to complete all of the weekly challenges each week, by the end of 2 weeks, we will have earned 11 tiers (5 OW1 levels) strictly through those weekly bonuses.
Looking at my playtime/my level, I’m getting about 53m 16s of match time per OW1 level (22,000 xp). Including queue times and drink/bathroom breaks, this averages to about 75 mins per level (observed from playing a lot recently in QP Flex queue; fast match uptime). Earning 20 OW1 levels (44 OW2 tiers) at a rate of 75m per level would take a total of 25 hours.
If I’m able to complete all 22 weekly challenges across the two weeks in the time it takes me to gain 20 OW1 levels (44 OW2 tiers), it would take 25 hours, or about 1.78 hours/day (1 hr 47m/day) to hit tier 55 in 2 weeks. And this isn’t including benefits from completing daily challenges, which could supplement any missed weekly challenges. Completing every daily and every weekly (with the speculated 3,000 xp from dailies) drops the daily average by another 10 minutes per day.
This doesn’t seem too outrageous, but it is a daily grind if you’re a F2P player wanting to play the latest hero on day 1 of competitive.
One other last note, it looks like completing every weekly will net roughly 540 coins per season. With every other battle pass including a hero, completing every weekly challenge should net enough coins to purchase the premium pass for every pass that includes a hero. This would circumvent the need to blitz through 55 tiers in a 2 week frame, and just allow the play to be focused on the weekly challenges. It’s all quite a bit of grind, but it’s technically feasible from what they’ve shown today, and barring the initial assumptions listed at the top.