There is an alpha polyfill effort here. https://github.com/FremyCompany/css-grid-polyfill
Regarding speed, here's the author's take.
> I wouldn’t say this polyfill is slow by any measure, but your mileage may vary on mobile devices. My advice would be to use the polyfill only on tablets and desktops at the moment, after you have tested the compatibility and performance extensively on a representative number of devices.
Also, there are js layout libraries used with similar functionality, so one can expect that it is possible to implement this feature with the same efficiency.