Glad that you asked your questions, and tried to answer your questions before you asked, it shows that you are serious with your questions.
First of all, IMO, the Buddhist universe has no beginning, with infinite time passed by. There were an infinity of Buddhas in the past, and an infinity of arahants were their disciples, and the world is still there, humankind is still there. Also there is a prediction that the Buddhism will disappear after 5000 years, so even you tried very hard, only a very small number of people will reach nibbana, don't worry. It is like you worry about if people keep drinking water, then the Earth will be dry
Secondly, in Buddhist cosmology, after a very long time, no matter what, the world will be destroyed. When it happens, devas and human will learn jhanas and be reborn as brahmas. Then after a very long time, the world will be formed again, and people after exhausted their kamma in brahma world will be reborn in that world. We were devas and brahmas in the past. The world will be formed, then exists a long time, then be destroyed again and again, it is the circle of life. All of your worry is like put a spoon of salt into to the ocean
Lastly, attain nibbana is not running away from the problem. The Buddha said that he sought every happiness possible in the past, he was the Chakravatin, the king ruled the world and lead people to happiness many times in the past, he lived luxury lives, he lived devas and brahman lives. But all of those things did not satisfy him, because he was not released from age, disease and death. He did not run away in fear, hid from the problem, but he was tired of worldly happiness. Most of people are like a poor men, are hungry and thirsty, and they don't know why a rich man with a comfortable life is bored with luxury food and drink and throw them away like nothing. If you don't understand the need of nibbana, no need to seek it, just seek mundane happiness until you are fed up with it, then you will know what nibbana means.
Please stop following me