Okay so hear me out.
I've counted the days when the patch should be released before the qualifiers by checking every TI qualifiers from the past
So based on previous TI qualifiers,
TI 2021
start of the qualifiers 06-23
Patch released 05-24 (it took 30 days, highly unlikely)
TI 2019
start of the qualifiers 07-07
Patch released 06-30 (it took 7 days, possible)
TI 2018
start of the qualifiers 06-18
Patch released 06-10 (it took 8 days, possible)
TI 2017
start of the qualifiers 06-26
Patch released 06-11 (it took 15 days, highly unlikely)
TI 2016
start of the qualifiers 06-25
Patch released 06-12 (it took 13 days, highly unlikely)
TI 2015
start of the qualifiers 05-25
Patch released 05-18 (it took 7 days, possible)
TI 2014
start of the qualifiers 05-12
Patch released 04-29 (it took 13 days, highly unlikely)
TI 2013
start of the qualifiers 05-13
Patch released 05-13 (the same day as the start of the qualifiers, possible)
TL;DR: Therefore, if we based TI 2022 from previous TI's(TI 2019, TI 2018, TI 2015 and TI 2013) the patch should be released 7-8 days before the start of the qualifiers or the same day as the qualifiers itself.
Credits to: liquipedia.com/dota2
Source: https://www.reddit.com/r/DotA2/comments/wv8gn1/to_spare_you_some_copium_and_hopium_the_patch/