It sounds like a problem at first glance but it isn't. For one, there's an easy solution: overbuild solar. With solar generation that is 2x-3x peak demand, you only need 4 hour storage to have a robust, clean grid with near 0 downtime. Add a bit of longer term storage and you've got a grid that's more reliable than the one today.

That's the conceptually simple solution, but ofc there's more practical ones. Mix in wind, some nuclear, different storage solutions (Ev2grid, pumped hydro, rocks-in-a-box, etc..), demand-side solutions (VPPs), efficiency improvements (insulation, heatpumps), a few of the hundreds of advanced projects being researched (solar in space, enhanced geothermal, iron air batteries, SMRs, etc..). Combine the 1000s of solutions being proposed, researched and scaled out and you have a very solid plan of attack.