The 21-year-old Alvarez birdied five of the final 13 holes on the East Course at Winged Foot Golf Club to finish at 3-under-par 67, the only sub-par round on Monday.
Americans Jason Hartwick, Luke List and Spencer Levin sit three strokes back in second place at even par. Hartwick and List also played the East Course while Levin finished with the low score of the day on the longer West Course.
Aron Price, 22, of Georgia, was one of four players to card a 1-over-par 71 on the day. Tom Glissmeyer, a 17-year-old out of Colorado who qualified for the 2003 U.S. Open, finished a stroke further back with a 72 along with eight others.
The 36 players that were unable to complete their rounds due to the lightning in the area will take to their respective courses early in the morning, while second round tee times remain unaffected.
Alvarez reaped the benefits of a fortunate tee time Monday, sandwiched in between periods of steady rainfall in the morning and late afternoon.
'I had a perfect time to play,' Alvarez said. 'The greens were quick, but soft. I was pretty lucky.'
Levin, one of the hottest amateur players in the country, also was able to escape the rain for most of the day.
'I'm happy with this as a first round,' said Levin. 'The main thing is just to get into match play.'
After the completion of the second round, the field of 312 golfers will be cut down to 64. Match play will decide the winner the rest of the way with a 36-hole final scheduled for Sunday.
The U.S. Amateur is one of 13 national championships conducted annually by the United States Golf Association, with 10 of the events strictly for amateurs.