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Hi - not endorsing them in any way as not used them but might be worth reaching out to these guys as they specialise in this https://speedboostr.com/services/ the owner of that company is on here as @JoesIdeas
BTW - to make site load a lot quicker on mobile, AMP is the way to go.
It sounds like what you're looking for is a headless server solution.
For example you could build your storefront out as a custom web app, then communicate with your shop via the Shopify API.
That gives you 100% control over your server + architecture and you can do things like cache pages and create the best solution for your individual store (rather than a theme that is used by many). It's more expensive than regular Shopify hosting but it's an option.
Another solution to help improve speed is to build a custom theme that's focused on performance, but that won't get you instantly loaded pages.
You can optimize your theme to help your load speed, this won't make pages load instantly but can help the user experience for mobile users or those on a slower connection. Here's a tool we built for analyzing and optimizing Shopify sites: Shopify Analyzer.
@JonWright 's suggestion about AMP works well if speed is your primary goal - these apply to mobile pages coming from Google search but can load them near instantly. You can probably set that up on your own: speedboostr.com/shopify-amp-guide.
If you need help with any of that send me a message.