Other things can be happening simultaneously with an Event, but they are never their own Event. By the very fact that this segment of time is represented by this Event, the player who created it is saying that this Event is the most significant or most defining happening in this part of the history.
You might think that you could say that an Event overlaps the span of time covered by another Event, but doing so would break the chronological independence of Events (because then you or other players can no longer put a new non-overlapping event separating any two events, as is a player's right during their turn). Therefore, when you create an Event, it must be a distinct Event that allows for an unspecified (potentially quite large) span of time between itself and its neighbouring Events.
Consider making it a separate Event
Sometimes you'll look at an Event and feel like it can't possibly be the most important happening during that span of time.
Then, perhaps your opportunity to make history should actually be used to create a new Event before or after. Simultaneity is rarely an important feature of bits of unrelated real-world history, except as a bit of curious trivia. Trust that the design of the game works, and that it's forcing you to keep Events separate for a good reason.
If you can possibly make your idea work without requiring that it overlap with another Event, place it as a new Event before or after. This makes your history more flexible, allowing the creativity of your fellow players to work with what you've created — and you do want others to use your contributions. Microscope isn't fun when your contributions are left untouched by others, and trying to exert perfect, precise control over how your creations interact with the rest of the history is just fighting against what the game is trying to do. A properly flexible history allows the other players to enjoy the full authority the game gives them on their turns. (Remember that during other players' turns, you are the "other players" in this paragraph! It cuts both ways.)
Handling truly concurrent happenings in the history
Remember that the already-created Event is, by definition, the most important or defining happening of that span of time. The player who created that Event got to that span of time before you did, and their authority for making that the defining Event of that span of time may not be contradicted or removed by later turns.
But in real history, things really do happen concurrently. To see such things during the game you need a Scene in the original Event.
Scenes allow you to explore bits of history that are concurrent with an Event, whether they're directly related or not. "Meanwhile in Houston, USA" might be a great way to start a Scene's Question inside an Event about, oh, say, the Vostok 1 spaceflight, for one example of a happening that's related but physically distant. This works just as well for completely unrelated happenings too, though: "Meanwhile, somewhere in China" is a fine way to start framing the location of a new Scene in an Event about, say, the Founding of Rome by Romulus and Remus.
If you simply want to add to the history, this will be a dictated Scene — but do consider, at least briefly, making it a Played Scene, as this gets other players invested in your creation and tends to create richer history than what you might come up with alone.
But why is that Event most important?
You might feel like the Scene that you just added was much more important. This isn't true! Why? Well rules-wise: because the Event was created first; that it's an Event means it's the most important event in that span of time; and making history earlier has the advantage that later history must not contradict it.
But that's just rules. What if the new happening really is more important? Answer: it isn't, it just looks that way now. Microscope histories often contain things that don't seem right, but are perfectly fine according to the rules. The game even tells you that this will happen, and what to do about it: Ask a Scene Question about it. (But, another Scene? Yes! Scenes snowballing by inspiring yet more Scenes just means your history has healthy momentum.)
"Why is [Event] the most important event at the time, despite [other thing]?" is a perfectly fine thing to wonder about. In Microscope, when you wonder about something in the history, you investigate it by playing or dictating a Scene.
A note on "important"
All this is in the context of your question about concurrency. Events don't have a specific "importance level" and don't have to match their neighbouring Events' levels of importance—the creating player's freedom to create whatever they want for the Event ensures that they will vary in "absolute importance" a lot.
But because you're specifically asking about concurrency and overlapping time, I stress the overriding importance of the existing Event as a way of promoting the idea of just accepting that it is the container for all other things happening at the same time. (In a more normal context where you're just playing the game, "importance" is not really the right way to look at it; primacy might be a more useful way to think of existing history.)
Don't fight the system
Embrace the constraints that Microscope puts on your creation. The constraints are there to spread authority among the players in a fair way and prevent the creation of history that becomes unpleasant to work with or near in later turns. The constraints also exist to fuel your creativity: the game forces you to think outside of your own box sometimes.
When you embrace these constraints that the game puts on you, you'll find that you end up creating things you wouldn't normally think of on your own. Creativity in Microscope is encouraged, but it's in partnership with the rules that limit you and in partnership with the other players. Go with the flow of the rules, and see what new places it takes you.