If you spend a lot of time alone, and do things alone, your colleagues will think that you want to be alone, or that you are anti-social / unsocial / asocial. Either way, they made the right decision and they respect your space.
If you want to fit into the culture and socialize with your colleagues, you need to adopt (at least partially) their way of being / doing.
The easiest way (for the beginning) is to copy their behavior related to the lunch break.
- How do they organize to go to lunch?
- Where do they eat?
- What do they eat?
- is there room at their tables?
Most likely, they ask around about who goes to lunch and where. Start doing the same. It can be as simple as asking around to your colleagues:
When are you gong to lunch today? I thought of joining you, I'm starving.
I am aware that doing something for the first time requires some effort and courage, but I am sure you have been through worse in your life, just like us all.
From here, once you broke the ice, go along with what goes on. Answer questions. Ask questions. Maybe even start using another desk in the room, so you are not alone.
It might happen that they do not respond according to your expectations. Do not worry. Give them time. Maybe they will feel cold, instead of friendly. That is normal. They are "afraid" of you in the same way you are "afraid" of them.
Even if some relationships just happen, many times it requires effort and time to build them. Any moment is a good moment to start building good relationships. And NOW is the best moment :)
Do not talk invite people to lunch early in the morning, or other stuff which might be misunderstood, or considered weird. There is no need to overdo anything.
Regarding change and how we can handle it better, there is a very good book (among others): "Who Moved My Cheese?" by Spencer Johnson. I recommend you warmly to read it. It is short, funny and useful.
It has been 3 days at my new company and I fee like I want to get out already.
Three days is a very short time. Think about this experience I had recently.
I work in a country where I do not know the language (except a few words and sentences). And they do not speak my language, and English is not the best skill they have. So usually I assume that my colleagues do not know English and mind my own business, while still being polite and having attempts at communication.
And a new colleague joined the company, he was assigned a desk just near mine. We said "hello" in the morning" and "good bye" in the evening and that was all.
UNTIL he wanted to prepare some tea, and needed to use my kettle. Not only that he asked in English, but he made the most complex and embellished sentence possible. So embellished and shocking, that neither of us was even able to remember it afterwards.
The moral? We did not communicate for several weeks, even though being closer than 1 meter (3 feet) from each other, only because we made the wrong assumptions, and were unwilling to break the ice of communication.
He proved to be a great guy, and we became very good friends starting with that very day.