Hi there,
Yes, this will be fine. Once you purchase your rail pass, you have to activate it in Japan at a JR station. When you activate it, you will have the choice of date of first use anytime within the following month. You can activate your Japan Rail Pass anytime up to 3 months from the date of purchase so you have lots of flexibility.
Please note that once activated in Japan and a starting date is set, it cannot be changed. A good way to ensure you get the right day is simply to activate your rail pass on the first date of travel if you are in a major city. A full list of all the JR stations where you can activate your Japan Rail Pass is available online here (with opening times). Many stations in Tokyo offer the activation service so you will have no problems.
Hope this helps!