Just put new strings on Am. Std. Telecaster and strings 1--4 rattle. Is there a quick solution? Raise bridge, tighten truss, replace nut, dunno?

J. Mayfield, I am going to guess that the string noise you are hearing is caused by the strings affected touching a fret or frets.
Without actually hearing it myself I can only guess. A loose or un-tightened truss rod makes noise but I have only heard one of those rattle if the guitar is shaken not when playing.
If it were a problem with the nut (slots cut too deep) a replacement could help but raising the bridge could be a quick fix at the expense of high versus low action.
A question would be, has this happened before after changing strings on this guitar? If that answer is no then perhaps this new set of strings is a heavier gauge and they could be hitting some frets that the lighter gauge strings did not touch with your guitar set up.
A lot of words written and not much said so far, I apologize for that Bro.
A good guitar tech could tell what to do, fret dress, bridge adjustment or just let the strings break in after a few days of playing and tuning to eliminate some new string slack but please let us know what happens.

_________________
you can save the world with your guitar one love song at a time it's just better, more fun, easier with a fender solid body electric guitar or electric bass guitar.

Thanks for the comments. I since have talked with my son who has not been available until now who is a professional guitarist(I taught him everything he knows--lol--just kidding). He agrees with you on your last statement--"Break them in and most probably the string rattle will go away". I will take your and his advice. Thanks again for your prompt reponse.

Give your new strings a bit of a streach along their length when fitting, nothing worse than constantly having to re-tune