The first question here is of course how you define the uptime of the site and how you measure your 99.9999 % SLA? Agreeing to a maximum downtime of 2 seconds per month is different from agreeing to 30 seconds per year, or 5 minutes over ten years. A simple DNS glitch for example might take a site offline for 2 seconds and might violate the first agreement but not the others.
Then how do you measure uptime? Up for whom? And where does the responsibility of the company end? If someone cuts a subsea Internet cable and takes a country offline (it happened before), does that violate the SLA? Depending on where the responsibility of the company ends the problem will become much more or much less challenging.
These points aside, I think if you want to build a very stable static site the most important ingredient is redundancy. I'd argue using a single CDN or cloud provider might give you good uptime but it will not ensure your downtime stays below 2 seconds per month, as a single outage of that provider will already be enough to break the SLA (and even CDNs like Cloudflare have outages).
What you could try is the following: Get your own IP space e.g. from RIPE or APNIC. Make deals with several hosting companies to announce that address space. Use several /24 subnets, announce each one via several of those companies. Create multiple DNS A records for all these subnets that your site's domain resolves to. Set the TTL of these records as high as possible to make sure recursive resolvers have them cached (and make sure your DNS servers won't be down for longer than your TTL). Put copies of your site on servers at all the hosting companies from where you announce your IPs.
I'm not a BGP expert so I don't know how fast routes will adapt to a single data center or server being down, if you have multiple A records most browsers should try them one by one if until one works (but does that count if it takes longer than 2 seconds?), so in theory there should be a good chance of your site staying up even if one of your data centers goes down.
Then again this assumes that you have everything on the server side perfectly under control. In my experience most of the system outages are caused by human error so the chance that you will destroy your own system by e.g. misconfiguring it is higher than that one of your data centers will be taken out by a nuke ;)
We're in the process of building such an anycast network and it's absolutely doable. I'll let you know if we reach 99.9999 % uptime.