Button Group for filtering time range with no default value selected

I'm working on a Timeline component at the moment, and by default, this timeline would show the activities/events for the day.

Users can select predefined time ranges such as the day, week, month, etc. Also, it has a date picker element that lets the user choose a custom date range.

The problem I'm facing here is that by default, the button group has a time range value of 'Today' selected. But when the user selects a custom date range value, the button group will have no value selected.

I know that button groups are similar to radio buttons and it's OK to have no value selected by default for radio groups when there is no possible accepted default value. (Such as payment options)

But does that work in Button Groups/Segmented Control?

Is there an established pattern for this scenario?