You are a special person! Almost everyone with this problem is flat put out by the fact they can't just open the CSV and have it work. They just won't do it any other way. Not only are you willing to copy and paste from the CSV, you're willing to bring it in to a column you went to the trouble of formatting as text. I congratulate you!
So, you can bring it in as text in a text column. If you're willing to do one more step, they can be dates in the format you desire (mm/dd/yyyy). Well, two more steps.
First, now change the format of the column's data. In the number format tab, choose the Date collection and then look under the format examples in the center of the tab. There is a dropdown UNDER the example choices in the center labelled "Locale (location):"... Scroll through it to "English (Australia)" and select it.
The date format examples above will change and you can select the exact version you want.
Of course, the text representation will not change. This is the real step. You need to force ("coerce") it. There are a LOT of ways to do this, but the APPROPRIATE one is to go to the Ribbon Menu, the Data tab. Find Text to Columns and click it.
Delimted or Fixed width doesn't really matter since if you go the Delimited route you'd select "no delimiter" by making sure nothing is checked and that'd end you up where Fixed width does: Step 3 of 3 in which you can set the type of format your column/s will have after conversion.
Choose the "Date" radio button and in the dropdown to its right, select DMY. You select what you want output, NOT what form the input is in.
Click "Finish" and the job is done.
For the future, you might want to look into Power Query. Since you have a nice CSV for the data, PQ would be the simplest thing to use. No formulas or programming, just it pulls the data from the file, ditches all the columns not needed, then converts the column of dates to... dates, and in the format you specify.
Save it all and any time you have new data to import, have it update its Table in your spreadsheet, or even have a helper spreadsheet to do this and import the results each time into the production sheet. If you have a helper page in the production spreadsheet (go this route and it would create one itself first time you "Load" its results), then copy and paste to the main sheet, or use formulas to copy the information over.
One can set up a button with a macro to update the Query, or even more, if you are able/allowed to use macros.
If nothing else, a "helper spreadsheet" that you load the converted dates into, then copy and paste from when you need them could be nice. But the above method would be pretty easy each time too, so... maybe six of one, half dozen of the other.