The phrase "a time when simply" is correct and usable in written English.
It can be used to refer to a specific moment or period characterized by simplicity or straightforwardness in a particular context.
Example: "There was a time when simply enjoying the outdoors was enough to bring happiness."
Alternatives: "an era when just" or "a moment when merely".
At a time when simply standing still could soon mean taking a slight step down there is perhaps good reason to question him again.
There was a time when simply being out qualified you as an activist.
Resolving this immigration challenge is important now – at a time when, simply put, we must attract a wide array of motivated and talented people from around the world to our culture of opportunity, even while cultivating our own homegrown talent.
It has over a second lag time when simply calling up your messaging window.
This would be an incredibly complicated process, with massive ripple effects (psychological as well as practical) throughout the entire economy, and this is one time when simply saying "we'll figure out the details later" doesn't suffice.
But remember this was a time when there simply was no other woman in Vienna (or almost anywhere else) doing anything comparable.
As much as I've grieved the deaths they had, my brain can't help but slip back into a time when I simply wished none of them was sick.
So Downton Abbey came out at a time when people simply wanted to escape on a Sunday night.
Nowadays, it's hard to conceive of a time when information simply could not be rapidly disseminated.
Under his new contract, our hours will become even longer, even more antisocial – at a time when we simply have nothing more to give.
"If we hit Al Qaeda hard enough and often enough, there will come a time when they simply can no longer replenish their ranks with the skilled leaders that they need to sustain their operations," he said.
