If we stick to the SDK, I don't know of a method providing this information directly; but there might be a way to derive this information from other resources. Again, if we stick to SDK, one "rather reliable" option is to use application usage statistics which Android OS saves during device lifetime. That is - the timestamp for a first "usage stats" ever saved.
This, though, clearly does not provide an exact "first boot time" timestamp, so it depends on whether some approximation is OK in your case. Generally, the problem with usage statistics is that Andriod aggregates it for periods distant in time - so, the older device is - the less accurate the date is. For example, for my current phone, first booted on Dec. 3 2014, aggregated usage statistics is first recorded on Dec. 21 2014 currently (for the record - it is Feb. 2016 by the time of this writing). (I have to admit though that I don't know how Android OS schedules the aggregation, and if it is just scheduled on Dec. 21 every year, or if it is indeed somewhat close to the first device usage - I guess it is easy to check with any other device.)
Following is some sample code showing UsageStatsManager usage, but it certainly would need more adjustments in order to address the fact of having more precision for more recent periods:
UsageStatsManager usageStatsManager = (UsageStatsManager) context.getSystemService(Context.USAGE_STATS_SERVICE);
Calendar year2013 = Calendar.getInstance(); year2013.set(2013, 0, 1);
List<UsageStats> stats = usageStatsManager.queryUsageStats(
UsageStatsManager.INTERVAL_YEARLY, // or adjust for "younger" devices to get more precision - so, you'll probably need several queries
year2013.getTimeMillis(),
Calendar.getInstance().getTimeInMillis());
// now, first element in stats (if it is present at all) will point to the "earliest" statistics saved *for this interval* (yearly in this case)
// use UsageStats.getFirstTimeStamp() to get first known/saved usage
Note also that, as documented in the SDK, UsageStatsManager
requires PACKAGE_USAGE_STATS
system-level permission, so you'll need to make user accept it in Settings first:
Intent settingsIntent = new Intent(Settings.ACTION_USAGE_ACCESS_SETTINGS);
startActivity(settingsIntent);
Hope it helps!