Advaita Vedanta and Buddhism both have 'non-dualistic' philosophies. Advaita literally means 'not two'. These two schools of thought have become separated over the centuries but are really no different at the core.
How did Gautoma become Buddha ? Not through Buddhism which didn't exist ! The texts tell us that he first went through deep meditation practices in various Hindu traditions and then through severe austerities.
By force of will he achieved his goal, but then saw that enlightenment is not to be found in meditation alone and that extreme austerity is not necessary, so he laid down his own path. The Noble Eightfold Path is not that different to other systems such as the 'Eight Limbs of Yoga'.
However by setting out the monastic code and living and teaching that way of life himself for 40 years he provided a monastic model that is virtually guaranteed to lead to realisation, even in the modern age.
What about those of us outside the buddhist monastery living in the advanced societies of the west ? Life opportunities and sense pleasures surround us.
Vedanta has more to say about life outside the monastery and while there is a risk of confusion there is also great potential benefit in exploring its philosophy in parallel.
Absence of a God provides a great attraction to many buddhists. Since the ultimate is inexpressible, Buddha minimised the conceptualisation of an almighty. However, what is the unconditioned or the unborn if not that ?
Being a Hindu tradition Vedanta often refers to the traditional Hindu gods and godesses. However they are all manifestations of the ultimate rather than the ultimate itself.
A salt doll went into the ocean to see how deep it was
How could it tell us about the depth ?
There are many people and therefore there are many paths. No religion should disparage another's path since they all have the same goal. Everyone is trying to gain more happiness and religion is simply the giving up of one form of happiness in search of a higher one.