Should I Continue Or Give Up?

Hello, I am a 26-year-old man. I recently met a girl my age. The story is quite long to tell, so I will try to shorten it. We met for the first time in a neighborhood pub and just met. We sat at different tables, with different companies. After about 2 weeks, however, she found me on Facebook and we started writing to each other. After a few days we went out and talked a lot, about things in life, etc. At our first meeting nothing happened, both the second and the third, but apparently she was interested in me. Two weeks after we first went out, it just came from inside me and I decided to buy a rose and leave it at the door. She was happy and immediately came home to have a drink, but again nothing happened. A month after we first went out, I decided to share my intentions with her and she explained to me, that she needs time, that she doesn't want to get into serious relationships now, and that she doesn't know what she wants. She also said that I was the first boy she liked after her ex-boyfriend. After that conversation, however, she stopped writing first, but always responded to my messages almost immediately. At each of my invitations to go out, she refused me with some stupid excuses. Basically, whenever we wrote to each other, she never answered me with a word or tried to end the conversation, whenever I asked her something, there was an answer on her part and she asked me something right after that. He always put on a smile or something after each sentence. The last time I wrote to her was on March 8th. I also wrote a rather large greeting message full of wishes and she answered me with only one thank you. Two days later, I saw her get into a boy's car. Five days ago, a friend of mine told me that he saw her enter her entrance with a boy (I think it's the same because he described it to me). My question is whether to believe that she needs time, because I guess she told me just so as not to spoil the relationship and try to re-establish a relationship with the girl or give up, because we still saw her 2 times with the same boy. I like it a lot, I like it a lot, but I have no intention of knocking on a door that will never open. Please advice, I will be infinitely grateful. Greetings that she told me just so as not to ruin our relationship and try to re-establish a relationship with the girl or give up, because we still saw her twice with the same boy. I like it a lot, I like it a lot, but I have no intention of knocking on a door that will never open. Please advice, I will be infinitely grateful. Greetings that she told me just so as not to ruin our relationship and try to re-establish a relationship with the girl or give up, because we still saw her twice with the same boy. I like it a lot, I like it a lot, but I have no intention of knocking on a door that will never open. Please advice, I will be infinitely grateful. Greetings