I am currently starting my online business. Right now, when someone places an order, I have to manually push it through to a wholesale company from where I am based and they handle the rest. I wonder, is there an application that automates this process for me? I am only aware of applications that are already using a wholesaler like AliExpress or Etsy. I want to add my own wholesale company to the software and that software will automatically push an order on my store through to the wholesale company of my choice.
It depends on this means for your workflow: "push it through to a wholesale company".
If you want to send an email to a company when a new order comes through, if the order contains products from that vendor, then you can use Order Automator, this is good for example if you use multiple vendors, and only want to send the items from each vendor, to the company... or if you want to send them a csv of orders for the day.
If you're just working with 1 company per order, then you could just set up email forwarding (you can set that up, for example in gmail).
If you're talking about integrating into a wholesale company's order system, then you would need to see if that company has an API available, then you can have a custom app built that connects your store to that company's API to place orders programmatically. But if going this route, first ask the company if they have a Shopify app, because some do (for example print on demand clothing apps in the app store work like this).