The quickest and easiest method to move your Microsoft Access Database online (to the cloud) is to deploy it on a hosted Windows Remote Desktop Server. You should be able to move to a Window Remote Desktop server with MS Access and be up and running on the same day! We have been providing terminal server (remote desktop) hosting solutions for over 15 years. Contact us and to discuss your options, pricing, MS licensing, etc. We host your Access database on its own server (not shared OS, not sharepoint) with resources dedicated to you. You will have a better experience hosting your MS Access database with us than other providers using a shared OS environment.
As previously announced by Microsoft, Access-based web apps (Access Web Apps) and Access web databases in Office 365 and Sharepoint Online were shut down in April 2018. See link here: Access Services in Sharepoint shut-down
You can also review our pricing calculator here: http://www.riptidehosting.com/Remote-Desktop-Hosting-Pricing.aspx
When comparing options for hosting your Access application online, ask the hosting provider if it will be a Windows Server with Remote Desktop Services or if they are hosting the Access application on a Sharepoint server. We do not provide hosting services on Sharepoint. If your MS Access application has VBA coding, it may not work in a sharepoint environment. You should also ask if your application is hosted in a dedicated OS environment (dedicated VM for you), or if it is on a shared OS environment, or if running on Sharepoint.