Slow down. Do it in a controlled, deliberate manner. It does not matter if the Gospel has started. Better to do this purposefully than to rush it.
Interestingly, this practice stems from the early church era and was initially only done by the bishop or priest about to proclaim the Gospel.
But, over time, the laity spontaneously adopted this gesture. A similar dynamic is at work when the laity mimic the priest’s orans posture at mass during the Our Father. That doesn’t bother me.
What I find puzzling is that most celebrants offer the sign of peace at the altar, hear “and with your spirit” from the people and then leave the altar to offer the sign of peace again to those nearby. That seems quite redundant and leave one to wonder if the celebrant really understands that part of the liturgy.