It is a delight to have your missionary here.
The P-day for the missionaries in the MTC is on Thursday, which begins one week after they arrive. They write their emails in the afternoon. That is when you can expect their first email.
Our experience has shown that packages from the US take up to 4 weeks or more to arrive and often arrive after a missionary has left for the field. We recommend that all packages be sent to where your missionary will be laboring. That way the package will be awaiting him or her when they enter their mission. It is difficult for us to forward packages to missionaries serving outside the city of Santo Domingo. Also for your information each time a missionary receives a package in the Deminican Republic, they will have to pay a custom fee, and it is about $2.50 a pound.