How is it possible in starting my cut phase, I gained 2lb in a week

Resuming or increasing exercise after a long-ish break (more than a small number of days) is likely to mean adding some water weight for muscle repair. If you're on a cut, your fat loss will outpace that on the scale fairly soon, possibly up to a small number of weeks depending on details.

Your profile says you're female. If you're of an age to have menstrual cycles, hormonal water fluctuations at certain points in the cycle can muddy the waters even further.

I tend to strength train seasonally, in my rowing off season. When I start lifting, I tend to gain a couple of otherwise unexplained pounds that hand around as long as I keep lifting progressively and consistently. When I stop in the Spring, I lose a couple of pounds with no other explanation. Not everyone has that pattern (some report ups and downs around - say - 3 times a week lifting). Also, I'm post-menopause, so I don't have the extra confusion of hormonal water retention.

I'd suggest you hang in there, carry on with your current plan for 4-6 weeks, and see how things net out over that kind of time horizon. If you have cycles, go for at least one full cycle so you can compare body weight at the same relative point in at least two different cycles. That should give you a better idea of what's really happening.

While you're patiently proceeding, I'd recommend you read this thread - especially the article linked in the first post - if you haven't already:

https://community.myfitnesspal.com/en/discussion/10683010/the-weird-and-highly-annoying-world-of-scale-fluctuations/p1

Best wishes for success - the effort is worth it!