Hi @TesDA ,
Actually, the search functionality within ComboBox is not case-sensitive. So when you type one character within the Searchbox, the ComboBox would list all items which contains that character.
As an alternative solution, I agree with @wyotim 's thought almost. You could consider custom the Search functionality of the ComboBox control.
I have made a test on my side, please take a try with the following workaround:

Set the Items property of the ComboBox to following formula:
Filter('20190325_case13', StartsWith(Title, ComboBox1.SearchText))
On your side, you should type:
Filter('YourDataSource', StartsWith(DisplayColumn, ComboBox1.SearchText))
Note: The DisplayColumn represents the column you want to display as Primary text within the ComboBox.
set the Primary text property of the ComboBox to your Displaycolumn as above screenshot.
Or
Filter('YourDataSource', ComboBox1.SearchText in DisplayColumn)
Above two formulas may cause a Delegation warning issue, it means that you could not delegate the data process to your data source, you could only process data locally. In default, you could only process 500 records locally at most, you could change the limit to maximum value -- 2000.
More details about changing the limits, please check the following article:
https://docs.microsoft.com/en-us/powerapps/maker/canvas-apps/delegation-overview#changing-the-limit
If the amount of records you populated within the ComboBox is not more than 2000, you could ignore this warning issue. If the amount of records you populated within the ComboBox is more than 2000, please check the following the solution mentioned within the following thread (save your data source records into multiple collections in bulk, then merge the multiple collection into single one collection, then use the merged collection as data source within your ComboBox😞
https://powerusers.microsoft.com/t5/General-Discussion/Pulling-in-large-ish-SQL-tables/m-p/243777#M71518
Best regards,