From your very own experience, has this been your case?
Did you start seeing results from between the 3rd and the 6th month?
Also, what kind of results exactly? Is it major traffic bump or one or two pages begin to pick up?
There's no definitive answer to this, due to numerous reasons. I'd prefer to advise new clients that expect 3-6 months, that way we often get results quicker, thus we under promise and over deliver.
Quite often I'll walk away from possible clients, who tell me " I need to be top 3 of page 1 in a month and I have $250 as a budget ", this follows on from my thread https://www.blackhatworld.com/seo/fastest-way-to-kill-your-business-taking-on-the-wrong-clients.1420630/post-15418165 and it's number 6 on the list.
I've recently been working with 3 or 4 new clients, who came onboard in June / July and we started getting results after a couple of weeks. These were in the main aged sites, just not been touched SEO wise, minimal content , fast loading, good UX etc.
I have another client who joined us in July, an expired domain, repurposed but in a totally different niche and this is a struggle to get what I'd like in terms of results. His new niche is quite competitive.
The issues with Google and their indexing rates don't help matters, so that is a big contributing factor for sure.
Just started working with someone in a difficult health niche, small budget of $500 but I informed this client before we started working, that their links they had were going to be the big issue as they were toxic spammy junk. 17k links to a site across a 24 hour period, all using the same anchor is not going to end well.
https://gyazo.com/ef41555261298105788b37026bf8afc8
They'd bought links and basically what they got was toxic PBN crap. So instead of us working from a clean slate, we are having to undo the crap already been done, before the results from our efforts kick in.
I also do think adding new content is important to help a site either brand new articles on new pages, or updating existing pages. I sometimes see clients in affiliate niches ranking for best XYZ 2022 keyword, but their page is still looking at 2022.