If you can create the object by resolving from the container or thru automatic injection, then go for it rather than manually instantiating it and then injecting dependencies using BuildUp. I don't see any Unity or dependecy injection stuff in your
code for Approach B though.
On your Approach A, you can configure the Initialize method to be automatically called as well as the value of its parameters when calling Resolve either through configuration or through API. This is called method injection.
When using the configuration approach, it would look something like:
<param name="param1" value="stringValue1" />
<param name="param2" value="stringValue2" />
When using the API approach, you would use the Injection method class. Or if you don't know the values of the parameter during registration, you can use pass a ParameterOverride instance in the call to Resolve.
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