You can create a trigger on Contact, pass as parameter 'before insert' and 'before update', because you want to fire such trigger everytime a contact is inserted or updated. In the trigger you can use Trigger.new to grasp all the new Contact records and store their IDs in a list. Later on you can create a method to do what you want and pass this list of IDs in that method. The method will execute the task of sending the email for all those contacts you passed in the method through their IDs. The following code is the skelectal/frame for tackling this issue. Disclaimer: I'm not 100% whether it works or not for your demand, but that's the implementation design which first came in my mind for this issue. I hope it can be helpful.

trigger TrgSendEmail on Contact (before insert, before update) {
    LIST<Id> listContactIDs = new LIST<Id>();
    
    for (Contact contact : Trigger.New) {
        listContactIDs.add(contact.Id);
    }
    
    if (listOfObjects.size() > 0) {
        SendEmail.sendingEmail(listContactIDs);
    }
}

public class SendEmail {
    public static void sendingEmail (List<Id> contactIDs) {
        LIST<sObject> listToDoSomething = [SELECT Id FROM Contacts WHERE contactId IN: contactIDs];
        
        for (Contact contact : listToDoSomething) {
            if (contact.Id != null) {
                // send the outbound message;
        }
    }
}