I'm not an expert ... but from my reading, if you start with really historically low levels of T (like I did), it takes a couple weeks for your body to make use of it.
As I understand it, your body needs to produce a shitload of androgen receptors -- the little gizmos that drag free T into the nucleas of your cell.
So even if you have lots of T in your blood serum, without the appropriate number of androgen receptors, you're in a holding pattern.
Speaking from personal experience, my "awakening" followed the standard timeline.
Google time course and TRT - the following is study paid for by Bayer.
Effects on libido, sexual desire, sexual thoughts and satisfaction with sexual life manifest after 3 weeks and plateau at 6 weeks
Changes in erections and ejaculations, sexual performance and satisfaction with erections usually achieved within 3Ã¢??6 months
Effects on quality of life evident within 3Ã¢??4 weeks and continue to develop for up to 18 months
Effects on depressive mood noted after 3Ã¢??6 weeks but may reach a maximum only after 18Ã¢??30 weeks
The time course for improvements in lipids varies:
Decreases in total cholesterol and triglycerides appear as quickly as after 4 weeks, but more commonly after 3 months or longer; a maximum may be reached after 12 months
Decreases in low-density lipoprotein (LDL) cholesterol may be slower, occurring after 3Ã¢??12 months, with a maximum reached after 24 months
Increases in high-density lipoprotein (HDL) cholesterol may occur after 3Ã¢??12 months, with further improvement for 12Ã¢??24 months
Effects on glycaemic control become evident after 3Ã¢??12 months, although insulin sensitivity may improve within a few days
Changes in fat mass, lean body mass, and muscle strength occur within 12-16 weeks and stabilize at 6-12 months, with marginal further improvements possible over years
Effects on bone mineral density are detectable after 6 months and continue for at least 36 months
Effects on inflammatory factors and endothelial markers noted within 3-12 weeks
Stimulatory effects on erythropoiesis are dose-dependent and apparent at 3 months, peaking at 9-12 months
Prostate-specific antigen (PSA) and prostate volume marginally rise, plateauing at 12 months; further increases may be related to aging rather than testosterone replacement therapy.