Dealing with conflicting deadlines for positions It often happens to have misaligned deadlines. E.g. the deadline for accepting a temporary position (say, for a fixed duration research assistantship) is before, but not by much, than the interview for another position.

One cannot with confidence refuse the first option, due to the aleatory nature of the interview to come which offers a competing/somewhat better position.

What is a good way to deal with such situation?

Is it a good idea/possible/usual to ask an extension on the first deadline?

Should one attempt to accept the first with a warning that you have a pending interview at some later stage? Should this have been disclosed previously (but I guess this would have led to not receiving the offer in the first place)

How orrible and damaging is to take the interview and eventually bail on the first position after accepting?

Alternatively, it might be viable to go to the interview and state that you are currently busy and ask if it is possible to move the starting date of the RA after the first job is over?
The key here is to communicate. It is perfectly fine to let either institution know that there is another position that you are interested in. Then try to work something out (prolonged response time, shift of an appointment, etc.) Normally, people are quite willing to show some flexibility.

After all, nobody has an interest in hiring somebody that already regrets signing up before he/she even started.