You can check the default files on the local/remote joomla installation at
/administrator/components/com_admin/sql/updates/sqlazure /administrator/components/com_admin/sql/updates/mysql /administrator/components/com_admin/sql/updates/postgresql
These folders contains SQL updates which will help in fingerprinting the version.
For instance: Joomla 3.8.3 will have all sql updates for previous versions till
3.8.2-2017-10-14.sql
similarly, for version 3.4.3
3.4.0-2015-02-26.sql
if you want to run brute-force to identify the version, following is the list of sql files you might want to run against:
2.5.0-2011-12-06.sql
2.5.0-2011-12-16.sql
2.5.0-2011-12-19.sql
2.5.0-2011-12-20.sql
2.5.0-2011-12-21-1.sql
2.5.0-2011-12-21-2.sql
2.5.0-2011-12-22.sql
2.5.0-2011-12-23.sql
2.5.0-2011-12-24.sql
2.5.0-2012-01-10.sql
2.5.0-2012-01-14.sql
2.5.1-2012-01-26.sql
2.5.2-2012-03-05.sql
2.5.3-2012-03-13.sql
2.5.4-2012-03-18.sql
2.5.4-2012-03-19.sql
2.5.5.sql
2.5.6.sql
2.5.7.sql
3.0.0.sql
3.0.1.sql
3.0.2.sql
3.0.3.sql
3.1.0.sql
3.1.1.sql
3.1.2.sql
3.1.3.sql
3.1.4.sql
3.1.5.sql
3.2.0.sql
3.2.1.sql
3.2.2-2013-12-22.sql
3.2.2-2013-12-28.sql
3.2.2-2014-01-08.sql
3.2.2-2014-01-15.sql
3.2.2-2014-01-18.sql
3.2.2-2014-01-23.sql
3.2.3-2014-02-20.sql
3.3.0-2014-02-16.sql
3.3.0-2014-04-02.sql
3.3.4-2014-08-03.sql
3.3.6-2014-09-30.sql
3.4.0-2014-08-24.sql
3.4.0-2014-09-01.sql
3.4.0-2014-09-16.sql
3.4.0-2014-10-20.sql
3.4.0-2014-12-03.sql
3.4.0-2015-01-21.sql
3.4.0-2015-02-26.sql
3.5.0-2015-07-01.sql
3.5.0-2015-10-13.sql
3.5.0-2015-10-26.sql
3.5.0-2015-10-30.sql
3.5.0-2015-11-04.sql
3.5.0-2015-11-05.sql
3.5.0-2016-02-26.sql
3.5.0-2016-03-01.sql
3.5.1-2016-03-25.sql
3.5.1-2016-03-29.sql
3.6.0-2016-04-01.sql
3.6.0-2016-04-06.sql
3.6.0-2016-04-08.sql
3.6.0-2016-04-09.sql
3.6.0-2016-05-06.sql
3.6.0-2016-06-01.sql
3.6.0-2016-06-05.sql
3.6.3-2016-08-15.sql
3.6.3-2016-08-16.sql
3.7.0-2016-08-06.sql
3.7.0-2016-08-22.sql
3.7.0-2016-08-29.sql
3.7.0-2016-09-29.sql
3.7.0-2016-10-01.sql
3.7.0-2016-10-02.sql
3.7.0-2016-11-04.sql
3.7.0-2016-11-19.sql
3.7.0-2016-11-21.sql
3.7.0-2016-11-24.sql
3.7.0-2016-11-27.sql
3.7.0-2017-01-08.sql
3.7.0-2017-01-09.sql
3.7.0-2017-01-15.sql
3.7.0-2017-01-17.sql
3.7.0-2017-01-31.sql
3.7.0-2017-02-02.sql
3.7.0-2017-02-15.sql
3.7.0-2017-02-17.sql
3.7.0-2017-03-03.sql
3.7.0-2017-03-09.sql
3.7.0-2017-03-19.sql
3.7.0-2017-04-10.sql
3.7.0-2017-04-19.sql
3.7.3-2017-06-03.sql
3.7.4-2017-07-05.sql
3.8.0-2017-07-28.sql
3.8.0-2017-07-31.sql
3.8.2-2017-10-14.sql
This may not give you the exact version but atleast helps you to identify the major version.