MongoDB: search by match of the input string or single words from the input string

I have field message in a collection messages, for example:

[
  {
   _id: "chrYMAqT8meXpqdrC",
   message: "Hello world. This is mongo"
  },
  {
   _id: "rKu5gf5zL6NaSvZ5Q",
   message: "Hello. This is mongo world"
  },
  {
   _id: "rKu5gf5zL6NaSvZ5Q",
   message: "world. This is mongo Hello"
  }
]

I want to search for messages where the message field contains /Hello world/ig or where the message field contains the words Hello and word. And most importantly - the words must be found in the order of the input string, so the last element in the collection must not be found, but the first two must. I know how to find by matching with regex, but in the second case i don't understand how to do it

you could use $regex with the regex Hello.*world. Also this

db.collection.find({
  message: {
    $regex: "Hello.*world",
    $options: "i"
  }
})

playground

or you could use $regexMatch

db.collection.find({
  $expr: {
    $regexMatch: {
      input: "$message",
      regex: "Hello.*world",
      options: "i"
    }
  }
})
])

options: "i" means case-insensitive. remove that if you don't want it

playground