Present underpants as the “pull up, pull down” step they’re already used to; the only thing that has changed is what they’re wearing.
Show your Big Kid a photo of themself as a baby in diapers. “Look how tiny you were when you were a baby. You still were in diapers. Now you are a bigger kid in Pull-Ups. Next, you’ll be in Big Kid undies, just like your cousin. Maybe one day soon you will want to pick out some undies when we go shopping.” Have them help shop for them if they’re interested, but don’t be surprised if it’s too overwhelming for your child. Nonchalantly bring home some cute undies, and let your child check them out when they’re ready.
Keep the new undies in the bathroom with their Pull-Ups. Remember that you want to keep the routine as close to identical as possible, so that your child is comfortable. After a few weeks, ask your child if they’re ready to try them. Sometimes, nervous children find it helpful to put their new underwear on over their Pull-Ups as they transition to Big Kid underwear.
When they’re ready, let them know what to anticipate so they can process the experience ahead of time. “Pretty soon you are going to want to try this new underwear. Yay! When you wear undies, it will be like Pull-Ups, but it may feel a bit different on the inside. Pull-Ups keep the pee in, but when you wear underwear, if you don’t make it to the toilet in time, the pee will drip down your legs. That happens sometimes when kids are learning to use the potty. It’s OK.”
Offer occasional suggestions to your shy child about using undies, but allow them to wear Pull-Ups as long as they like. Pushing a introverted toddler to progress faster than they are ready can cause resistance. Deep down, they really do want to get the hang of this potty training thing; they’re just very cautious about it. They will decide they’re ready to move on when it’s the right time for them.