Absolutely. Key for me was to invite children's friends (and family) along, host it in our house and make it a recurring weekly thing. The books (presumably you also have these from the MSRI's 'Mathematical Circles Library') are great, but week-to-week I've found the free online NRICH resources much more directly useful: https://nrich.maths.org/about-nrich
It's been really rewarding. I definitely recommend jumping in. I started with my reception-age child (+ school friends), and have just extended it to their younger sibling (+ friends from nursery). Your 3.5 year old will have started the EYFS (Early Years Foundational Stage) syllabus at nursery if they attend (which is also what they do in the 'Reception' year at primary school, before starting the national curriculum in the first year), so they will now be exposed to counting and comparisons. The perfect time to get started, in other words!
There's some NRICH funded research that showed that exposure to symmetry and reasoning at this level was much more predictive of future abilities than numbers and counting. I think when parents try and help at the early stages, they often try to e.g. get their kids to count to 100, which is conceptually identical to counting to 10.
For number fluency there is the free White Rose '1 minute maths' app, which does a very nice job of gamifying subitising & etc. A lot of primary schools in London seem to have adopted the White Rose teaching resources.
https://whiteroseeducation.com/1-minute-maths
Practically speaking (running a little maths circle in the UK for my children, and some of their friends from nursery and primary school), I have found the Nrich website to be the single best source of resources:
https://nrich.maths.org/about-nrich
The book by Zvonkin described in the article is a very good motivator, particularly for the honest descriptions of lessons gone badly wrong, and staying up late cutting out pieces of cardboard! But it's quite difficult to use as a teaching resource.