We need a database developer to help with creating indexing system for MySQL database

The goal is to get the database ready to be searched using indexing. And, if you are able to actually implement this in the front-end for the feature, this would be ideal. 
Here is a short video of what we are trying to do: [login to view URL] What needs to be searched: 
 In our platform, we need individual users to be able to search everything within the platform. But, very specifically for a feature, or an action. An example of this would be “Edit invoice #1234 for project: Slawson”. The current issue with the developer we have is they are not a database developer, and are concerned that the ability to query the whole databse may cause the system to be slow, or cause the search to have crazy load times for those queries. However, we are not needing the designer to query the whole database because its just information within their own system, where indexing comes into play. It should only query what is in that users account specifically. How they will search: In our new system, they will be using a search bar (see video). ultimately, we need help connect it to the app but in a way that is performance-focused. 
Something to note too: when a user is searching or using this tool, we would also make it where an example query would be: “Edit invoice [number] for [project]” whereas for the project, they would be required to enter the first digits of the project and the system would display the query of all projects in that account matching those three first letters. Another example would be “Edit [client]” whereas they would be editing that client record. So when they start typing the first three letters of that client it will only query and display those that match those three for that users account specifically. Here is a list of all the queries we would need. 
 Key:
[client] client name [vendor] vendor name [number] number specifically identifying the searched query. [project] specific project. [purchase order] specific purchase order [task] task name [milestone] milestone name