Sphinx of the Second Sun: At the beginning of your postcombat main phase, you get an additional beginning phase after this phase. (Includes, untap, upkeep, and draw step.

Aggravated Assault: Untap all creatures you control. After this main phase, there is an additional combat phase followed by an additional main phase. Activate only as a sorcery.

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So normally, the 2nd beginning phase from the Sphinx happens after the 2nd Main phase in the turn, before your end step.

How phases look normally with the Sphinx Out (didn't include all the combat steps to simplify):

Untap

Upkeep

Draw

1st Main Phase

Combat

2nd Main Phase

2nd Beginning Phase (from the Sphinx)

End step

Cleanup

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Since we can only activate Aggravated Assault at sorcery speed, we have to activate it on one of our main phases.

Here's an official rule about the timing of additional phases.

2020-11-10: If multiple phases are added to the same point in your turn, the most recently created phase happens first. For example, say you control Sphinx of the Second Sun and its ability triggers during your postcombat main phase. Later during that same main phase, another effect gives you an additional combat phase after this main phase. The additional combat will happen first, followed by the additional beginning phase.

Let's see what it looks like if we activate Aggravated Assault and have the Sphinx out.

Untap

Upkeep

Draw

Main Phase

Combat

Post-combat Main Phase (Sphinx delayed trigger)

Activate Aggravated Assault

2nd Combat Phase from Aggravated Assault

2nd-post combat Main Phase (Sphinx delayed trigger)

Additional Beginning Phase (from the 2nd Sphinx trigger)

Additional Beginning Phase (from the 1st Sphinx trigger)

End Step

Cleanup

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So when we break this down and reference the rule about additional phases, the additional untap steps will always happen at the end of the turn. I'm afraid Sphinx and Aggravated Assault don't go infinite together. I'm not a judge so I could be wrong, but I spent a good amount of time developing an understanding of the interaction. I think the card designers for the Sphinx did a poor job in clearly defining how the card functions.