Can anyone remind me how many days had passed since the beginning of the story?
Chapter 1 is the day of the switch, caused by head injury. Amnesia cases tend to be subject to observation and testing, so Sou was there at least a week before his discharge in chapter 3. From chapters 4 to 12, it's at least two days, probably a week (most people won't go to the conbini first or second day in a new house after a hospital stay). Chapter 14 is a new day, chapter 15 is same day. Chapter 16 is at least a week after hospital discharge, probably two. Chapter 18 is probably a month after the discharge, since it's time to go donate sperm (most obligations like this have exceptions for trauma). My guess is that chapter 20 is mid-week to weekend, probably midweek. Chapter 28 is at least a month later, since his muscle training is making him buff, and that takes at least 4 to 12 weeks.
Chapter 29 reveals it is currently May 202X, so we can confirm Sou's birthday is between January and March (monthly sperm donation begins after 16th birthday, OG Sou was there once, our Sou was there once, and we take into account passage of time). Chapter 32-34 is the day after the first refusal to send Sou to school first day, we also see Sou has become much stronger. Chapter 36 is too vague, dunno how much time passed, but 39 is probably the day after 36. It's a week to process admissions paperwork, probably two.
First day of school is chapter 42. Chapter 82 is day 2 of school. School holiday in chapter 133 is interesting. Summer holidays start late July, yet Sakura's school also has a school holiday. Probably a local holiday or school founding day. Chapter 140, same day, second depicted sperm donation, which is regular enough for Sou to be well-known at this point, so at least four times, possibly more. Chapter 144 is day 3 of school. Hijinks! Day 3 ended on Chapter 257. Chapter 258-262 would have been Day 4 of school, but our boy Sou was confined. Per chapter 263, it took three more days after that for Sou to deal with his family and the school. So it is Day 8 of the school entrance arc, Day 4 of actual school.
Rough timeline:
March 202X: Sou's birthday, first sperm donation, "amnesia", comes home, recovery
April 202X: second donation, starts working out
May 202X: asks to go to school
June 202X: goes to school <---we are here, probably second week of June