The sentence "once approved, we will proceed" is correct and usable in written English. You can use it when you are referring to something that needs approval before it can move forward. For example, "Once the project is approved by the board, we will proceed with implementation.".
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Once we had an initial explicit shape estimation, we will proceed to 3D depth estimation.
Once both teams reach an agreement level of 90%, we will proceed to screening the full set of titles and abstracts.
Once an agreement level of 90% is met within each pair, we will proceed to the full set of articles.
I will tell you why, and then we will proceed.
"Everyone will be informed how we will proceed very soon.
As soon as the delay is removed, we will proceed".
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com