I would like to make this recipe but I don't have 'instant espresso powder' I have coffee in powder, or I can make an espresso cup with it. Is the...

If you have instant coffee powder rather than instant espresso powder, that'll work fine, just use a little extra. If you have ground coffee beans they will impart coffee flavor but a gritty texture even when ground to as fine a powder as possible. I loathe the texture, but it seems not to bother most people so it should be fine to use it.

I don’t know if your recipe calls for a sugar syrup to be added to the buttercream to sweeten it, but if so, you could use coffee for the liquid when making the syrup.
I had leftover coffee and turned it into coffee syrup, which I use to sweeten iced coffee and to add to desserts (tiramisu, anyone?).
The other think you could try is putting the sugar and coarsely ground coffee in a food processor and grind both till fine, imbuing the sugar with coffee flavor and helping the sugar dissolve more quickly when beating it into the butter.

Thank you very much Nancy! ^^

similar question addressed here...
https://food52.com/hotline/39500-can-i-use-ground-coffee-instead-of-instant-espresso-powder-for-muffins