There is no syntax that does precisely what you're looking for. As you've already laid it out, you can create a lambda that has Foo as its receiver either by creating it as you're passing it into a function that takes such a lambda:
fun useFooExtension(fooExtension: Foo.() -> Unit) {
    fooExtension(Foo())
}
useFooExtension {
    println(this is Foo)
}
Or by specifying the type of the variable explicitly, like so:
var foo1: Foo.() -> Unit = { println(this is Foo) }
However, you can declare a lambda that takes a Foo as its first parameter, with this explicit lambda syntax (the variable type is only here for explanation purposes, it's otherwise redundant and is inferred):
var foo2: (Foo) -> Unit = { foo: Foo -> println(foo is Foo) }
And these two types of lambdas are actually cross-assignable, because the extension on Foo really just takes that Foo as its first parameter under the hood as well. So you can do all of these things:
foo1 = foo2
foo2 = foo1
useFooExtension(foo1)
useFooExtension(foo2)
There is one difference between the two types: if you want to call them with a Foo instance, you can only call foo1 as an extension, but you can call both of them as if they took a Foo as their first parameter. So these are all valid calls:
Foo().foo1()
foo1(Foo())
foo2(Foo())