Can I change My Start Date?

start date can't be changed without starting a new account (as far as I'm aware)

You can change your start weight though.
From website:
Go to "Apps"
Go to "Tickers"
Click "Update Your Weight Data"

or

Go to "Check In"
Click "Edit Previous Entries"
Then delete the old entries that you don't want anymore

You don't need to delete old entries, you just have to "trick" the program by adding a new entry at least one day older than your current oldest date/weight, because the weight loss/gain calculations pull the oldest date/weight data.

You must use the Web version, not the mobile apps, to update your starting weight or edit previous entries. On your mobile device, you can use the Web browser and request to load the desktop site.

Navigate to APPS > Tickers > Update your weight data. Enter your desired starting weight and click Save Changes. That will update the oldest date/weight in your profile.

Alternately, navigate to MY HOME > Check-in > Edit Previous Entries.

a. Enter a new value in the Starting Weight text box and click Change; or

b. Scroll down and click on the highest page number to take you to the oldest date/weight entry. Once you find your oldest date/weight entry, under Add New Entry, enter the new date/weight and click Add New Entry. That will replace the oldest date/weight with your new one.

c. If you want to keep all of your historical data, Add New Entry at least one day older than the oldest date/weight.