To exist means to exist in time
Not necessarily. Hawking showed that time actually had a beginning. That beginning was at the moment of the Big Bang.
Prior to the Big Bang there was an existent singularity, "outside" of time.
which means to be found somewhere and able to interact with other existing things during a series of consecutive instants (duration).
Found somewhere perhaps, though even that somewhere cam be hard to make meaningful to us, but a moment of no duration does not define what time is. An infinite multitude of moments of no duration will do no better in defining time. Add any number of moments of no duration together and all's you'll get is a moment of no duration.
"Consecutive instants"? Consecutive to what? Cause and effect get a bit tricky at the quantum level. Physics is having a very hard time determining why we seem to perceive an "arrow of time" in which things can be defined as consecutively related phenomena. Physics has yet to answer the mysteries of the directionality of entropy. This so called flow to time breaks down at the quantum level. From the point of view of physics, the future is as real and existent as the past and present. It is only the "flow of our awareness" that delineates the past, present, and future.
It should also be noted that change can be of no duration. It can be instantaneous, as when an electron jumps from one state to another for instance.
We are equipped to perceive macroscopically. At this level we are deluded into believing we are experiencing causes in reality instead of merely the effects of realistic causes. We perceive the pictures movement. We don't perceive the flipping pages giving us the delusion of that movement.
Realistically it may be that past, present, and future are collectively a moment of no duration having simultaneous existence.
To be real is to exist in space and time and to interact with other real things.
Not exactly. The singularity was real yet was the originator of space and time not a subject of those things.
Everything that can be said to exist meets all three criteria. Nonexistent things meet none of them, and there is no middle ground where something possesses only one or two of those qualities.
I don't think this is correct. As presented above. Nothing in science bars a real singularly unique entity's existence which has no interaction with other real things since none exist other than itself. Science indicates that Space and time as we know them in our universe both had beginnings -or at least the phenomena we've labeled with those terms - whereas there is no indication that their originator did. The singularity existed in neither space nor time as we define them.
What space is, is not so easily described. What space does is a little easier to define with such tools as Einstein and the quantum crew developed. And so it is with time.
Existing "outside of time" is a claim made by many about things like gods. For me, nothing that exists does so outside of time.
Since you mentioned gods, let me attempt to explain what is meant by the Christian God being outside of time...
All created creatures in this universe experience time sequentially as their sentience becomes aware of moments of no deration which that sentience passes through. The "direction" of that passage is dictated and sustained by God. That would be defined as being within and subject to a sensory flow of time.
This would be in contrast to God's sentient awareness of all of time at once - past, present, future - as a single instantaneous realistic moment. Yet...in comparison to the singularity of the Big Bang we say that God while aware of and simultaneous experiencing all of existence is not itself subject to its restrictions - that is restrictions of awareness of or ability within time and space but is instead the originator of those things.
Nothing in science precludes God from being able to exist prior to the beginnings of time or space as we have come to define those things.
We don't so much exist "in" time but instead we become aware of reality in a dictated sequence.