We employ Application Performance Management to structural monitor the performance of company applications, including SharePoint Online. Via APM we observed a severe effect of initial login to Office 365: it structural adds up to 8 seconds to the actual SPO activity, for all of our worldwide locations:
And via the same structural APM measuring this week we noticed that the effect of initial login was largely improved, to a mere 2 seconds. We analyzed what changes were done on our side that caused this performance improvement. Turns out that a general policy update was applied in which multiple Office 365 URLs, including that of our SharePoint tenant, were added to IE trusted sites. This workplace change has a significant positive effect on the Office 365 network access times, and it also results in situation with federated login that IE automatically logs the user in.