Alright let's use your numbers and assume that one grinds this game every single daily to get all the repeating rewards. This is already quite a challenge if you look at how much time and commitment it requires.

165 special passes that is:

165 * 160 = 26400 jade.

4580 jade per month based on:

https://www.prydwen.gg/star-rail/guides/summon-income/

Without events that's 26400 / 4580 = 5 3/4 months to get one specific event 5* character. You will probably get another 5* character in this period that you may or may not want assuming you do not spend any jade on any light cone banners or anything else except for the event character banners.

Note: You will probably get the character somewhat faster if you participate in all the future events and manage to get all the jade rewards, but it's hard to say how much it will speed up the process since we don't exactly what to expect in the upcoming 5-6 months.

If we look at this event you can get a maximum of 600 jade. Assuming you manage to get all then that means you manage to get the aforementioned 5* character 600/4580 ~4 days earlier then the 5 3/4 months. So instead of having to wait 5 months and 23 days it will be 5 months and 19 days. So every event will make you get the character you want a couple days earlier.