In short: No, without a bot no way for now.
Detailed explanation:
In order for you to send users messages on telegram you would need to create your own telegram bot. They have a well documented API which you can read and play around with.
There are 2 things you should know about sending messages to users using telegram bot:
You can't just send random people messages on telegram even if you know their phone number, to send them messages you need to have their chat_id. See how in the docs
To get the chat_id the user must first click the start button that comes up when they open your bot for the first time. Telegram will send you the chat id of that user and you save it for later when you would want to send messages to that user.
There are tons of libraries that makes working telegram bots very easy, it wouldn't take you more than an hour to get started.
I hope this answers the question, feel free to ask further questions, I have made some bots and you can also play around with them to see how it works.
Cheers )