When the Bhagavatam speaks of Krishna assuming a human form, are we to understand this as a process in time or rather as one of Krishna’s eternally existing features? If the latter is the more appropriate perspective, is it not inaccurate and misleading to employ phrases like: ‘Krishna assumed a human form’ etc??
I believe this topic is discussed in the Caitanya Caritamrta. On the one hand, Krishna comes in His eternal spiritual form. But He also makes ‘adjustments’ so that conditioned souls can see Him, and also so that He can play the role of a human being. For example, the Bhagavatam 1.1.20 states that Krishna appeared ‘kapata-manusha’, ‘pretending to be human.’
‘Assume’ in the relevant sense here means ‘to take or begin to have.’ In that sense we can say that Krishna takes or begins to have certain humanlike features in His spiritual form, such as visibility to conditioned souls, or typical human behaviors, such as dropping His Sarnga sword in a battle or lamenting over the apparent loss of His parents.
The above is a general response, however I do suggest you investigate the matter further in the Caitanya-Caritamrta.