This might sound unreal but Bitcoin takes approximately 1.3 years to get to a new ATH. if we consider the halving dates and then check the new ATH, as an average it concludes. I am not speculating anything as it is a simple calculation of the average. just take a look:
Your approximation is correct when we see the past ATH's but we not yet aware about the coming ATH and it could take place after halving for sure but still we can't determine an exact date for that event. I'm sure that after the halving event Bitcoin's price will continue to gain some momentum and it will continue to grow to good levels within short duration, but still it's next ATH is expected around 2024's last quarter to 2025's last quarter.
Yes, we can't say that the ATH will happen in 2025's first quarter because that predication will most probably be inaccurate. But, surely it will happen within 2 years after halving and once we see next ATH then once again we may see another bear market. The simplest reason that why Bitcoin reaches its ATH is when new people learn about it and they invest in it and when media or influencers promote it. Those type of promotions will be common after the halving event and people will once again invest a lot of money in whole crypto market to gain profits.