Hi! Thank you for this question.
The sense of isolation felt while living in a country other than your homeland (be that where you were born, raised, or have citizenship... if those are diffetent) is a real struggle and decreases longevity in your new locale. Every social activity or any activity that takes place among people (like grocery shopping) can become a reminder of all the friends you don't have.
I'm no expert but one thing I'm learning is to use my cultural ignorance as a benefit. I like men's fashion in general so I compliment guys (cashiers, mostly) on their Omani rings, watches, and other apparrel as an opportunity to practice the Arabic I've learned and see if anything comes from it. A guy recently asked for my number so he could give me an agate stone for a ring! It's since come out that he would like my advice in business so it's tempting to feel like he's trying to ended me to himself so I'll be obligated to share all my know-how with him. But "quid pro quo" isn't necessarily bad... it's just as true that my compliment of his ring was coercive, hoping for a friendship - benefitting from his time rather than his wisdom. It's a 2-way street so go easy on others and yourself. At the very least this I an opportunity to discover a cultural way of bartering deals.
Another thing I just touched on... learn some Arabic. So many people are surprised when I rattle off a greeting in local Arabic phrases and pronunciation since I'm very white. I'll never truly blend in but occasionally I'll be asked "Are you Egyptian? Lebanese? Surely you're from the Levant!" English is a linguistic status marker - like you're tongue is flying 1st class. But Arabic feels more like home to locals so even if you only learn a little bit it can help open the door for relationships.
Another thing is to be authentically yourself. As expats, it's easy to find ourselves put into a box of "American" or "foreigner" when meeting locals. So it's vital that you don't just let that happen. Maintain your interests and hobbies OR search for new ones you really love! I've gotten into Arabic calligraphy because I love art. I've got a friend who takes his guitar and djembe camping so he and his local friends can share songs. If you like cars or video games take the time to find out what's popular here and why; you may find a new game, place to visit, or some friends in the process.
Making friends isn't just about connecting through an activity. As Father John Behr put it, "Communication is veiling and unveiling in the give and take of understanding." Veiling and unveiling sounds odd but it's all about expressing yourself in a way that will resonate with your audience. I like tattoos but that won't resonate much with Omanis so I switch to art, another interest - one interest is veiled so that my personality can be revealed with greater clarity to the guy in front of me. But I'm still me.
Don't let the loneliness make you lose yourself in order to fit in. Stay curious, friends. We're in this together.