B737-900 Captain reported they failed to make a crossing restriction departing SEA because a wake turbulence encounter prompted them to reduce their climb rate to minimize their exposure to the wake.

Narrative

We were cleared the Mountain 2 Departure out of SEA. Our takeoff weight was 185;000. We briefed the departure requirement of crossing NEZUG at or above 4;000 ft. as a threat; and voiced that the requirement should not be a problem if we delayed our acceleration and prioritized the crossing altitude. During the takeoff the winds were light and the outside temperature was about 85. The Tower cleared us for takeoff behind an A320 with minimal spacing between us. Climbing through 3;000 ft. we encountered [the A320's] wake which started to roll our aircraft left and right. I was the flying pilot; and elected to reduce pitch since we were too slow and heavy to increase pitch to climb above the wake. Our pitch reduction allowed us to duck back underneath the wake and resume flying in safe; smooth air. However; this pitch reduction also caused us to cross NEZUG at approximately 3;400 ft.We were also unable to ask ATC for relief at NEZUG because the radio chatter was too busy to interrupt. Our intent was to make the NEZUG crossing restriction at or above 4;000 ft.; however; I elected to reduce pitch to avoid the aircraft wake which caused us to miss the crossing altitude. This conscious decision was made in the name of safety. We showed no other aircraft near us on TCAS or visually that we became close to during our climb. When cleared for takeoff close to another aircraft; we don't know that aircraft's weight; thrust; anticipated climb technique; etc. Awareness; judgement; and adjustment of our aircraft in the name of safety sometimes cause us to modify the initial plan during the flight.