Is embracing Islam available for all people?

Yes, Islam is available for all people. Every child is born with a sound natural disposition, worshiping Allah without a mediator (being a Muslim). So he, without the interference of family, school, or any religious authority, worships Allah directly until the age of puberty, when he becomes competent for religious duties and is held accountable for his deeds. At this time, he either takes Jesus as a mediator between himself and Allah and becomes a Christian, takes Buddha as a mediator and becomes a buddhist, or Krishna and becomes a Hindu, or takes Muhammad as a mediator and, thus, deviates totally from Islam, or remains on the religion of Fitrah (sound natural disposition) worshiping Allah alone. The one who follows the message of Muhammad (may Allah's peace and blessings be upon him) that he conveyed from his Lord is following the right religion that conforms to the sound Fitrah, and anything else is considered deviation even taking Muhammad as a mediator between oneself and Allah.