1) Write data to DRAM.
2) Read data from DRAM.
3) Verify that data matches.
4) Buy an oscilloscope.
You are on a fool's errand. What if there's a problem with the interface? How will you possibly debug it without a scope or logic analyzer? How will you know if the design is marginal and is just barely working?
You might do functional testing at varying supply and
temperature, looking for environmental margin. But
you will not gain any info about what failed or why,
only the application envelope of the assembly.
High speed DDR has signal integrity sensitivities and
attaching a 10pF 'scope probe to later generations
stands a chance of messing up the eye and causing
the failure you're looking for. "A scope" may not be
the equipment you're looking for (or to avoid).
You might do functional testing at varying supply and
temperature, looking for environmental margin. But
you will not gain any info about what failed or why,
only the application envelope of the assembly.
High speed DDR has signal integrity sensitivities and
attaching a 10pF 'scope probe to later generations
stands a chance of messing up the eye and causing
the failure you're looking for. "A scope" may not be
the equipment you're looking for (or to avoid).
That’s why they make high speed active oscilloscope probes.
But that’s only part of the equation. We’re all assuming here that the OP is talking about DDR RAM; they haven’t actually said so. It could be a data converter or something else. Also, the issue of probing a BGA is problematic. This is not a trivial problem.