The TR answer to this question appears to be “No.”
I believe The Canons of Dordt answer this question in the affirmative, only it does not use the word “assume”, but rather it says that parents “ought not doubt.”
Article 17: The Salvation of the Infants of Believers
Since we must make judgments about God’s will from his Word, which testifies that the children of believers are holy, not by nature but by virtue of the gracious covenant in which they together with their parents are included, godly parents ought not to doubt the election and salvation of their children whom God calls out of this life in infancy.
Now, taking into account the “P” in TULIP (I argue as a TR), if we can have faith that had our infants died in their infancy, their election would be sure, why then can Christian parents not hold that same faith in regard to their children who live past infancy?
See Also On Faith and Presumption for an explanation of the difference between faith in God’s promises and “assumption”.
Sola Fidelity 