This will get you 90% of the way there ; )
window.$ = document.querySelectorAll.bind(document)
For Ajax, the Fetch API is now supported on the current version of every major browser. For $.ready(), DOMContentLoaded has near universal support. You Might Not Need jQuery gives equivalent native methods for other common jQuery functions.
$.ready()
DOMContentLoaded
Zepto offers similar functionality but weighs in at 10K zipped. There are custom Ajax builds for jQuery and Zepto as well as some micro frameworks, but jQuery/Zepto have solid support and 10KB is only ~1 second on a 56K modem.
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