How do you build an owned audience?
Ask at the moment of highest trust, which is the order. An email address, a notification permission or an app install requested at checkout converts several times better than the same request in a pop-up.
In more detail
Then use it for something worth receiving before you use it to sell. A list that only ever hears about discounts becomes a list that only opens during discounts.
What to do about it
A channel that works at small spend often stops working at large spend, because the cheap audience runs out first.
Paid traffic is rented and gets more expensive every year. Every channel you own — email, notifications, your own audience — gets cheaper as it grows.
Attribution is harder than the dashboards suggest. A customer sees six things and the last one takes the credit.
The mobile app angle
Push notifications sit on the owned side of that line, which is the whole commercial argument for an app.