Using some and includes

if (substrings.some(v => str.includes(v))) {
    // There's at least one
}

Example

var paragraph = "some things never change"; 
var substrings = ["random", "never", "test"];

if(substrings.some(s => paragraph.includes(s))) { 
	console.log("substring found")                 
} else {                     
	console.log("NOT FOUND");                 
}

output: substring found

Take not that The includes() method performs a case-sensitive search to determine whether one string may be found within another string, returning true or false as appropriate.