If you want to manipulate the amount of data that is downloaded to users' OST files, this can be set via Group Policy.
You can use the Group Policy templates, which are available from the Microsoft Web site (see https://technet.microsoft.com/en-us/library/Cc178992.aspx for more information). The Group Policy template files are Outlk15.admx and Outlk15.adml. If you use Group Policy to manage this setting, the following registry data is utilized by Outlook.
Registry Key: HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\15.0\Outlook\Cached Mode
Value: integer value (Decimal) specifying the number of months (use only the following values)
0 = All (entire mailbox)
1 = one month of email items
3 = three months of email items
6 = six months of email items
12 = twelve months of email items
24 = twenty-four months of email items
If you are concerned with bandwidth when DeploymentPro is being used to configure Outlook profiles at cutover (which in turn will also download the OST file to each user's local drive), you could set this to either 1 or 3 months before your MX record cutover, and then increase this number in the subsequent weeks, post-migration, so that users will then have a larger portion of their mailbox downloaded and synched with the local OST file.
For Outlook 2016+ clients, there is a newer ADMX for Office 2016. This ADMX has newer settings, which means you can limit the cache to days, not just weeks/months. https://www.microsoft.com/en-us/download/details.aspx?id=49030
GPO Location: Microsoft Outlook 2016\Account Settings\Exchange\Cached Exchange Mode
Reg Value HKCU\software\policies\microsoft\office\16.0\outlook\cached mode!syncwindowsetting
Description: Select Cached Exchange Mode sync settings for profiles
Default: One year
Possible Values: [0, Three days] [0, One week] [0, Two weeks] [1, One month] [3, Three months] [6, Six months] [12, One year] [24, Two years] [36, Three years] [60, Five years] [0, All]