How could I initialize the @State variable in the init function in SwiftUI?

Property wrappers are generating some code for you. What you need to know is the actual generated stored property is of the type of the wrapper, hence you need to use its constructors, and it is prefixed with a _. In your case this means var _mapState: State<Int>, so following your example:

import SwiftUI

struct MyView: View {
    @State var mapState: Int

    init(inputMapState: Int)
    {
        _mapState = /*State<Int>*/.init(initialValue: inputMapState)
    }

    var body: some View {
        Text("Hello World!")
    }
}