Yes, ebooks are available immediately after you have purchased them online. For example, if you have purchased on Amazon, then it will appear in your Kindle device list within 30 seconds.
From an author/publisher point of view, it may take between 3 to 10 business days for an ebook to be available for sale on the platform where you have submitted it for publication. On Amazon, it takes up to 3 days at the most. If there is an error or something objectionable has been found while checking by the platform, then you will get notified accordingly. Once you have corrected the error, then the ebook goes back into the queue for checking again and will get published if all is ok. This can again take up to 3 days on Amazon and up to 10 days on other platforms as per their standards.