error TS2339: Property ‘x’ does not exist on type ‘Y’

If you want to be able to access images.main then you must define it explicitly:

interface Images {
    main: string;
    [key:string]: string;
}

function getMainImageUrl(images: Images): string {
    return images.main;
}

You can not access indexed properties using the dot notation because typescript has no way of knowing whether or not the object has that property.
However, when you specifically define a property then the compiler knows that it’s there (or not), whether it’s optional or not and what’s the type.

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Edit

You can have a helper class for map instances, something like:

class Map<T> {
    private items: { [key: string]: T };

    public constructor() {
        this.items = Object.create(null);
    }

    public set(key: string, value: T): void {
        this.items[key] = value;
    }

    public get(key: string): T {
        return this.items[key];
    }

    public remove(key: string): T {
        let value = this.get(key);
        delete this.items[key];
        return value;
    }
}

function getMainImageUrl(images: Map<string>): string {
    return images.get("main");
}

I have something like that implemented, and I find it very useful.