Given the timeline’s mentioning of Natasha being paid by Bob to walk Chris to the bus stop in middle school I would assume it probably happened early on in high school. With Chris being the basketball team’s water boy beginning freshman year, Bob almost certainly had to have had some involvement in at least wrangling Chris’ retardation at the school early so he wouldn’t end up the punching bag bitch boy like a nerd character in an 80’s high school flick. When parents get involved in school early on, they end up knowing kids quicker and who among them is more compatible with their own kid, or in Chris’ case “most likely to sympathize with retardation”. Regarding your point I always found it funny that Chris never brought up explicit dates when he started being “friends” with these girls simply because he’s the type to hyper focus on that.
Well it seems I have found you an answer in my boredom.
According to
https://sonichu.com/cwcki/Gal-Pals_and_Past_Sweethearts_(CWCipedia_page)#The_Women_in_my_Life a page written by Chris:
She was a good girl and a good friend to me back in Manchester High. We shared a few classes, and sat at the same lunch table one year or two.
Additionally, if we follow this link, it brings use to the year 1998, Chris' junior year, and since we know that Kellie and Sarah were his lab partners, we can possibly assume the Kellie and Sarah were the ones involved in the worksheet.
https://sonichu.com/cwcki/Manchester_High_Leaks#Getting_Acquainted
It would seem that the "Gal-Pals" were mostly a construct of his Junior and Senior years. The pictures we have of Chris only shows him with them when he was getting a bit older. Natasha, according to those links, Chris knew since Middle School, making her the oldest friend of the Manchester lot. It's completely possible that Bob's payment to Natasha occurred before. Natasha is also a year older than Chris.
Additionally, I dug into the Cwcki and found this about his fellow Waterboy. A lot of Chris' waterboy pictures are him looking younger, but this puts a bit of a date on his friendship with Joseph. He's also supposed to have been born in 1979, 2 years and a couple months older than Chris.
He had this to say about Laura
I did not meet her until my Freshman Year at Manchester High (she was a Cheerleader then); she was two grades ahead of me, and apparently she went to Providence Middle and was in the same class as me during my time, but she advanced to High School about 7th Grade. She was a pretty girl; I had a crush on her that one year.
TLDR: Here is a timeline based on evidence we have:
Pre-1996 (probably 94): Natasha Turner becomes friends with Chris
1996: Chris becomes loose friends with Joe Herring, a fellow Waterboy.
1996: Chris has a crush on Laura Dorazio.
1997: Joe Herring is no longer referenced anywhere, Chris is over Laura Dorazio. Joe may have graduated or, given circumstantial evidence of lack of Waterboy pictures, Chris quit the job and stopped seeing Joe.
1997: Possibly the end of his Friendship with Natasha Turner do to her smoking. He claims she got off the bus and went smoking with her friends. It's unlikely she shared the short bus, and unlikely the short bus and regular bus arrived at the same time.
1997: Chris gets demoted to the short bus by fighting an African American.
1998: Chris becomes friends with the Gal-Pals, t's likely around now Bob started the payment system to the Gal-Pals, given what happened with Natasha both working out well but her role ended in Chris' life.
2000: Chris graduates and loses contact with all but Kellie.
2001: Chris stops talking to Kellie
No evidence shows the Manchester girls appearing prior to 98, except 1 anachronistic reference in Sonichu 7 where Kellie shows up in 1996 as a cliffhanger never to be mentioned again. The timeline seems to suggest that Natasha was paid as early as middleschool until the short bus incident and the gal pals about a year after that (maybe as a result of it).
Either that or Bob wanted Chris to do something "manly" with the boys and since Chris is inept at sports it was the waterboy. In retrospect he should have forced Chris to join an art club or computer club if they had one. Something more aligned with his interests.
Its the lack of dates, like you said, that makes me wonder when Bob made the arrangements and why I asked the question. It could have been something from the start where he knew Chris was incapable of making friends and surviving in the real world and got some girls to babysit his son throughout High School or it could have been something he came up with in Senior year when Chris still had no friends and was still being picked on. Just strange that Chris never mentioned something like this or really sad if he obsessed for ten years over people he knew for a few months.