Quickest way to note the current time I occasionally need to note the current time so I can quickly check it later, for example the time I arrived at some place. I don't care how it's stored since I don't keep it long term.
Previously I used the alarm functionality of the Clock app - when adding an alarm, the initial value was the current time. Unfortunately they updated the app and now it defaults to the next hour or something, so I have to manually adjust it.
I agree with Irfan Latif's suggestion in the comments that taking a screenshot is the quickest way. That said, I'm suggesting a little bit sophistication on this, so as to justify this answer!
My suggestion is that you add up a quick tile in your Quick Settings. Preferably, among the first four or five tiles that shows up when you swipe down from the status bar. Customize it in a manner so that whenever you would tap/press that quick tile it would log the then datetime in a text file. Whenever you feel the need to look the time log you can see it by opening the file in any text editor. Better, if you append the file instead of overwriting it, you would have all the timelogs at your disposal.
I'm suggesting MacroDroid automation app for this, primarily because it is free (price) to try and test the solution.
Instructions:

Install the app and launch it.

In the main window, scroll down until you see a box/tile titled Quick Settings Tiles.

Tap on it, and do the following:

In Macrodroid tile 1 field enter this text : Log time.
Tick Button.
Tick Collapse on Press.
Turn the slider rightwards to make it Enabled


Edit your Quick Settings to add MacroDroid tile named Macrodroid tile 1 in the visible quick tiles. This step may differ depending upon your ROM. If you need help do a web search such as &quot;How to configure/customize quick settings in&quot; followed by the name of your device.

In the main Macrodroid window, click on the box/tile Add Macro.

Set Triggers, Actions and Constraints as follows:

Trigger: Macrodroid specific → Quick Settings Tile → Log time → Toggle On/Button Press

Action: Files → Write to File:

Use pencil icon to choose location for your text file, or leave it to default location /storage/emulated/0 (this is the internal storage / sdcard location that shows up when a file manager is started)
in the filename field, type logtime.txt
in the Enter text field, type [month] [dayofmonth], [year] - [hour 12]:[minute]:[second] [am_pm]\n
tick Append to file


Constraints: leave them untouched



Name the macro to whatever you want.

If you have not done this already, make sure to exempt Macrodroid from battery optimization settings, or it won't work reliably! This step may differ for your ROM. If you have difficulty getting the app battery optimization exempted, do a web search.


At this point everything is ready. Swipe down from the status bar to access  Quick Settings and tap/press that Log time tile you had added. Now, go into your file manager to the location where you intended the text file to be saved (in step 6). It should be there. Open it, and the datetime would be noted there. It should look something like this:
May 20, 2021 - 12:01:10 PM

New datetime would be appended in a new line every time you would tap/press that quick tile. If you don't want the file to be appended, untick &quot;Append to  file&quot; option in the action for your macro.
Tip: you can add another action in your macro to give you a audio/visual or both of the hints that the macro has run. For example, after the file writing action, you can add another action that should play a sound or show a notification. Such actions are available in Macrodroid.