Non Married Visa for Australian Citizen and an EU Citizen

[Roady]

I am currently coming to an end of my tier 5 youth mobility visa and would like to stay to live with my partner who is lithuanian. We have been together for 20 months but have not been living together as she has been living in estonia to complete her studies. She is planning to move to the UK in July/August and we are exploring to possibility of obtaining a spouse visa to allow me to stay.
Is there any chance for a visa to be obtained in these circumstances. And are there any things such as living together in estonia for 3 months before applying
I am an australian citizen who was able to earn £48 000 in the last tax year but cannot find an employer who can provide a tier 2 sponsor

[Plum70]

Is your partner a dual national (British being the other)? If not then the spouse visa route will not work.

Using the EEA route might work if you both can show that you have an active relationship akin to marriage with co-habitation (this seems to be a criteria for the UK). Evidence like a joint tenancy agreement, bank account statements, utility bills should be proof enough. But as you say that you have not been living together, these may not be viable options.

So...what supporting evidence do you have at the moment and how long left on your Youth mobility visa?

[Greenie]

The UK requires two years cohabitation for a couple to be considered in a 'durable relationship' under the Eea regulations, which according to the op, they don't have.